Training large language models (LLMs) efficiently while preserving model quality poses significant challenges, particularly with subbyte precision supported by state-of-the-art GPUs. Current mixed-precision training approaches either apply uniform precision to all GEMM operations or rely on heuristic-based methods that fail to generalize during training, leading to suboptimal convergence and instability.

Deep learning (DL) based methods have become increasingly attractive in image motion estimation applications. In this study we investigate the use of a noise-to-noise (N2N) training strategy for improving the robustness of a DL motion-estimation network in the presence of high imaging noise in the image data. This strategy is based on the rationale that the image motion estimated from one noisy measurement of a given image pair should be equally applicable for registering the image pair when it is obtained from a different noisy measurement. In the experiments we demonstrated the proposed approach for motion-compensated noise suppression in cardiac-gated SPECT imaging, where we utilized the image data acquired from 237 clinical cases at 50% reduced dose. The proposed N2N approach yielded an average reduction of 18.5% in the mean-squared-error (MSE) of the gate frames compared to a traditional training approach. It also achieved a more uniform performance among the different cardiac phases in spite of their statistical image variability.

Recent work demonstrates that structured patterns in pretraining data influence how representations of different concepts are organized in a large language model’s (LLM) internals, with such representations then driving downstream abilities. Given the open-ended nature of LLMs, e.g., their ability to in-context learn novel tasks, we ask whether models can flexibly alter their semantically grounded organization of concepts. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, can models infer these novel semantics and reorganize representations in accordance with them? To answer this question, we define a toy “graph tracing” task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.), and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization of representations according to the graph’s structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, which shows getting non-trivial performance on the task requires for the model to infer a connected component. Overall, our findings indicate context-size may be an underappreciated scaling axis that can flexibly re-organize model representations, unlocking novel capabilities.

Prior work has shown that text-conditioned diffusion models can learn to identify and manipulate primitive concepts underlying a compositional data-generating process, enabling generalization to entirely novel, out-of-distribution compositions. Beyond performance evaluations, these studies develop a rich empirical phenomenology of learning dynamics, showing that models generalize sequentially, respecting the compositional hierarchy of the data-generating process. Moreover, concept-centric structures within the data significantly influence a model's speed of learning the ability to manipulate a concept. In this paper, we aim to better characterize these empirical results from a theoretical standpoint. Specifically, we propose an abstraction of prior work's compositional generalization problem by introducing a structured identity mapping (SIM) task, where a model is trained to learn the identity mapping on a Gaussian mixture with structurally organized centroids. We mathematically analyze the learning dynamics of neural networks trained on this SIM task and show that, despite its simplicity, SIM's learning dynamics capture and help explain key empirical observations on compositional generalization with diffusion models identified in prior work. Our theory also offers several new insights---e.g., we find a novel mechanism for non-monotonic learning dynamics of test loss in early phases of training. We validate our new predictions by training a text-conditioned diffusion model, bridging our simplified framework and complex generative models. Overall, this work establishes the SIM task as a meaningful theoretical abstraction of concept learning dynamics in modern generative models.

It has been observed that message-passing graph neural networks (GNN) sometimes struggle to maintain a healthy balance between the efficient / scalable modeling of long-range dependencies across nodes while avoiding unintended consequences such oversmoothed node representations, sensitivity to spurious edges, or inadequate model interpretability. To address these and other issues, two separate strategies have recently been proposed, namely implicit and unfolded GNNs (that we abbreviate to IGNN and UGNN respectively). The former treats node representations as the fixed points of a deep equilibrium model that can efficiently facilitate arbitrary implicit propagation across the graph with a fixed memory footprint. In contrast, the latter involves treating graph propagation as unfolded descent iterations as applied to some graph-regularized energy function. While motivated differently, in this paper we carefully quantify explicit situations where the solutions they produce are equivalent and others where their properties sharply diverge. This includes the analysis of convergence, representational capacity, and interpretability. In support of this analysis, we also provide empirical head-to-head comparisons across multiple synthetic and public real-world node classification benchmarks. These results indicate that while IGNN is substantially more memory-efficient, UGNN models support unique, integrated graph attention mechanisms and propagation rules that can achieve strong node classification accuracy across disparate regimes such as adversarially-perturbed graphs, graphs with heterophily, and graphs involving long-range dependencies.

Approximate nearest neighbor (ANN) query in high-dimensional Euclidean space is a key operator in database systems. For this query, quantization is a popular family of methods developed for compressing vectors and reducing memory consumption. Among these methods, a recent algorithm called RaBitQ achieves the state-of-the-art performance and provides an asymptotically optimal theoretical error bound. RaBitQ uses 1 bit per dimension for quantization and compresses vectors with a large compression rate. In this paper, we extend RaBitQ to compress vectors with flexible compression rates - it achieves this by using B bits per dimension for quantization with B = 1, 2, ... It inherits the theoretical guarantees of RaBitQ and achieves the asymptotic optimality in terms of the trade-off between space and error bounds as to be proven in this study. Additionally, we present efficient implementations of the extended RaBitQ, enabling its application to ANN queries to reduce both space and time consumption. Extensive experiments on real-world datasets confirm that our method consistently outperforms the state-of-the-art baselines in both accuracy and efficiency when using the same amount of memory.

Motion compensation is an effective approach for reducing motion blur and suppressing noise in cardiac gated imaging. In this work, we propose to introduce a temporal regularization measure in optimization of a deep learning (DL) network for motion compensation in cardiac-gated SPECT images. This introduced measure is used to exploit the temporal consistency in the physical motion of the myocardium among consecutive phases of the cardiac cycle. In the experiment we demonstrated this approach on a set of 197 clinical acquisitions with imaging dose reduced by $50 \%$. The results demonstrate that the proposed approach can lead to improved motion compensation accuracy among all individual gates by the DL network, with an average reduction by $6 \%$ in the mean-squared-error of the motioncompensated myocardium, indicating that the proposed approach can be more robust in combating the excessive noise level in reduced dose imaging.

Motion compensation is effective for reducing motion blur in cardiac gated imaging. In this work, we investigate the potential benefit of incorporating an anatomical similarity measure in training a deep learning (DL) network for motion compensation on cardiac gated SPECT images, which are known to suffer from limited data counts and exhibit image intensity distortion (due to partial-volume effect) associated with cardiac motion. In this similarity measure we utilize the spatial image gradient to characterize the correspondence of boundary points on the left-ventricular wall between two gate frames. In the experiment we demonstrated this approach on a set of 197 clinical acquisitions, and the results show that with the proposed approach the DL network can improve the anatomical similarity among the gate frames upon motion compensation.

Recent work has observed an intriguing "Neural Collapse'' phenomenon in well-trained neural networks, where the last-layer representations of training samples with the same label collapse into each other. This appears to suggest that the last-layer representations are completely determined by the labels, and do not depend on the intrinsic structure of input distribution. We provide evidence that this is not a complete description, and that the apparent collapse hides important fine-grained structure in the representations. Specifically, even when representations apparently collapse, the small amount of remaining variation can still faithfully and accurately captures the intrinsic structure of input distribution. As an example, if we train on CIFAR-10 using only 5 coarse-grained labels (by combining two classes into one super-class) until convergence, we can reconstruct the original 10-class labels from the learned representations via unsupervised clustering. The reconstructed labels achieve 93% accuracy on the CIFAR-10 test set, nearly matching the normal CIFAR-10 accuracy for the same architecture. We also provide an initial theoretical result showing the fine-grained representation structure in a simplified synthetic setting. Our results show concretely how the structure of input data can play a significant role in determining the fine-grained structure of neural representations, going beyond what Neural Collapse predicts.

Recent work has revealed many intriguing empirical phenomena in neural network training, despite the poorly understood and highly complex loss landscapes and training dynamics. One of these phenomena, Linear Mode Connectivity (LMC), has gained considerable attention due to the intriguing observation that different solutions can be connected by a linear path in the parameter space while maintaining near-constant training and test losses. In this work, we introduce a stronger notion of linear connectivity, Layerwise Linear Feature Connectivity (LLFC), which says that the feature maps of every layer in different trained networks are also linearly connected. We provide comprehensive empirical evidence for LLFC across a wide range of settings, demonstrating that whenever two trained networks satisfy LMC (via either spawning or permutation methods), they also satisfy LLFC in nearly all the layers. Furthermore, we delve deeper into the underlying factors contributing to LLFC, which reveal new insights into the permutation approaches. The study of LLFC transcends and advances our understanding of LMC by adopting a feature-learning perspective.

With the merit of self-sustainability, ambient backscatter aided wireless networks (AmBWNs) have attracted considerable attention for the potential application in Internet of Everything. The ambient backscatter transmission significantly reduces the power consumption by reflecting or absorbing ambient RF signals to transmit at the cost of fragile performance guarantee. The dual-mode node which can transmit in active mode (ATM) or backscatter mode (BTM) has been proposed to improve both energy efficiency and performance reliability. In the AmBWN composed of dual-mode nodes, information flows and energy flows coexist and are transferable. Existing maximum flow algorithms designed for static networks absence of frequent node and link state transitions are not suitable for AmBWNs. Therefore, we investigate the statistical guarantee of the maximum flow in evolving AmBWNs with energy constraint, flow conservation and Markov inequality constraint. The simulation result shows that the proposed statistical maximum flow algorithm can improve the energy efficiency by 2.5 times under poor channel condition.

Deep learning denoising methods have been found to be effective for noise suppression in reduced-dose studies in medical imaging applications. In this work, we investigate the feasibility of improving the generalizability of a denoising network by using a dose-blind training approach, in which the network is trained with a loss function defined to accommodate the varying data statistics associated with multiple reduced-dose levels. In the experiments, we demonstrated this approach on quarter- and eighth-dose data from a set of 895 clinical cardiac SPECT perfusion imaging acquisitions. The quantitative results show that a dose-blind denoising network could generalize well over both dose levels, and outperformed dose-specific training in detection of perfusion defects at both quarter- and eighth-dose data (p-values-4; paired t-test).

Motion compensation is an effective approach for noise suppression and motion blur reduction in cardiac gated SPECT imaging. In this work, we investigate the potential benefit of using a deep learning network for motion compensation in a sequence of gated images throughout the cardiac cycle in the presence of large inter-subject variability and imaging degrading factors. We make use a set of clinical acquisitions from 130 subjects and quantify the motion compensation accuracy by variants of two known cascaded learning networks (namely VTN and VoxelMorph). The results in the experiments show that both networks can yield accurate compensation results in both standard dose and half dose studies. Specifically, VTN achieved a relative MSE of 0.0312 (full dose) and 0.0561 (half dose), compared to 0.0340 (full dose) and 0.0356 (half dose) for VoxelMorph. Both networks also outperformed the classical optical flow equation (OFE) method.

Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle to balance between resisting the oversmoothing that may occur in deep models, and capturing long-range dependencies of graph structured data. Moreover, the complexity of this trade-off is compounded in the heterogeneous graph case due to the disparate heterophily relationships between nodes of different types. To address these issues, we propose a novel heterogeneous GNN architecture in which layers are derived from optimization steps that descend a novel relation-aware energy function. The corresponding minimizer is fully differentiable with respect to the energy function parameters, such that bilevel optimization can be applied to effectively learn a functional form whose minimum provides optimal node representations for subsequent classification tasks. In particular, this methodology allows us to model diverse heterophily relationships between different node types while avoiding oversmoothing effects. Experimental results on 8 heterogeneous graph benchmarks demonstrates that our proposed method can achieve competitive node classification accuracy.

Deep learning models such as the Transformer are often constructed by heuristics and experience. To provide a complementary foundation, in this work we study the following problem: Is it possible to find an energy function underlying the Transformer model, such that descent steps along this energy correspond with the Transformer forward pass? By finding such a function, we can reinterpret Transformers as the unfolding of an interpretable optimization process. This unfolding perspective has been frequently adopted in the past to elucidate more straightforward deep models such as MLPs and CNNs; however, it has thus far remained elusive obtaining a similar equivalence for more complex models with self-attention mechanisms like the Transformer. To this end, we first outline several major obstacles before providing companion techniques to at least partially address them, demonstrating for the first time a close association between energy function minimization and deep layers with self-attention. This interpretation contributes to our intuition and understanding of Transformers, while potentially laying the ground-work for new model designs.

Cardiac SPECT perfusion imaging is important for diagnosis and evaluation of coronary artery diseases. However, the acquired image data can suffer from motion blur due to patient respiratory motion. We propose a maximum-likelihood estimation (MLE) approach to determine a surrogate respiratory signal from short-time acquisition frames for motion correction. To compensate for the low data counts in the short-time frames, we employ a regularization term to exploit the similarity in acquired data among neighboring acquisition angles. In the experiments we validated this approach first on a set of simulated phantom data with known respiratory motion, and then on clinical acquisitions from 17 subjects. The results demonstrate that the proposed MLE approach could yield a reliable respiratory motion signal even with the acquisition frame duration being as short as 100ms, and outperformed both center-of-mass and Laplacian eigen-maps methods.

Deep learning (DL) denoising has recently found applications in a wide range of important problems in medical imaging. A practical challenge encountered in clinical applications is that the acquired image data can exhibit great variability in terms of noise level among different subjects. In this study, we investigate whether it can be beneficial to exploit the varying data statistics among different subjects in a DL denoising network. We propose a modified loss function in the form of a weighted sum of mean-squared-errors for DL training in which the contribution from individual subjects is adjusted according to their noise levels. In the experiments we demonstrated this approach with a set of 895 clinical acquisitions in cardiac SPECT studies with 50% of standard dose. The quantitative results show that the proposed approach can further improve both the regional accuracy of the reconstructed left ventricle and the detection accuracy of perfusion defects.

Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of graph heterophily or adversarial attacks. To at least partially address these issues within a simple transparent framework, we consider a new family of GNN layers designed to mimic and integrate the update rules of two classical iterative algorithms, namely, proximal gradient descent and iterative reweighted least squares (IRLS). The former defines an extensible base GNN architecture that is immune to oversmoothing while nonetheless capturing long-range dependencies by allowing arbitrary propagation steps. In contrast, the latter produces a novel attention mechanism that is explicitly anchored to an underlying end-to-end energy function, contributing stability with respect to edge uncertainty. When combined we obtain an extremely simple yet robust model that we evaluate across disparate scenarios including standardized benchmarks, adversarially-perturbated graphs, graphs with heterophily, and graphs involving long-range dependencies. In doing so, we compare against SOTA GNN approaches that have been explicitly designed for the respective task, achieving competitive or superior node classification accuracy. Our code is available at https://github.com/FFTYYY/TWIRLS. And for an extended version of this work, please see https://arxiv.org/abs/2103.06064.

Data availability is one of the most important performance factors in cloud storage systems. To enhance data availability, replication is a common approach to handle the machine failures. However, previously proposed replication schemes cannot effectively handle both correlated and non-correlated machine failures, especially while increasing the data availability with limited resources. The schemes for correlated machine failures must create a constant number of replicas for each data object, which often neglects diverse data popularities and does not utilize the resource to maximize the expected data availability. Also, the previous schemes neglect the consistency maintenance cost and the storage cost caused by replication. It is critical for cloud providers to maximize data availability (hence minimize SLA violations) while minimizing costs caused by replication in order to maximize the revenue. In this paper, we build a nonlinear integer programming model to maximize data availability in both types of failures, and therefore minimize the cost caused by replication. Based on the model's solution for the replication degree of each data object, we propose a low-cost multi-failure (correlated and non-correlated machine failures) resilient replication scheme (MRR). MRR can effectively handle both correlated and non-correlated machine failures, considers data popularities to enhance data availability, and also tries to minimize consistency maintenance and storage cost. Extensive numerical results from trace parameters and experiments from real-world Amazon S3 demonstrate that MRR achieves high data availability, low data loss probability and low consistency maintenance and storage costs when compared to previous replication schemes.

Lowering the administered dose in SPECT myocardial perfusion imaging (MPI) has become an important clinical problem. In this study we investigate the potential benefit of applying a deep learning (DL) approach for suppressing the elevated imaging noise in low-dose SPECT-MPI studies. We adopt a supervised learning approach to train a neural network by using image pairs obtained from full-dose (target) and low-dose (input) acquisitions of the same patients. In the experiments, we made use of acquisitions from 1,052 subjects and demonstrated the approach for two commonly used reconstruction methods in clinical SPECT-MPI: 1) filtered backprojection (FBP), and 2) ordered-subsets expectation-maximization (OSEM) with corrections for attenuation, scatter and resolution. We evaluated the DL output for the clinical task of perfusion-defect detection at a number of successively reduced dose levels (1/2, 1/4, 1/8, 1/16 of full dose). The results indicate that the proposed DL approach can achieve substantial noise reduction and lead to improvement in the diagnostic accuracy of low-dose data. In particular, at 1/2 dose, DL yielded an area-under-the-ROC-curve (AUC) of 0.799, which is nearly identical to the AUC = 0.801 obtained by OSEM at full-dose ( p -value = 0.73); similar results were also obtained for FBP reconstruction. Moreover, even at 1/8 dose, DL achieved AUC = 0.770 for OSEM, which is above the AUC = 0.755 obtained at full-dose by FBP. These results indicate that, compared to conventional reconstruction filtering, DL denoising can allow for additional dose reduction without sacrificing the diagnostic accuracy in SPECT-MPI.

In computerized detection of clustered microcalcifications (MCs), the individual MCs in a mammogram image are typically identified by a pattern classifier based on the local image features at a location under consideration. In this work we investigate a hierarchical learning approach for detection of clustered MCs in which we exploit the property that the individual MCs in a cluster region tend to appear in close vicinity of each other. In the experiments we demonstrated the proposed approach on a set of 542 mammogram images and evaluated the detection performance by using free-response receiver operating characteristic (FROC) analysis. The results show that the proposed approach could effectively improve the detection accuracy by reducing the level of false positives (FPs).

4D image reconstruction can significantly improve the image quality in cardiac-gated imaging using single-photon emission computed tomography (SPECT). However, it is also associated with increased computation complexity which prevents it from being widely used in the clinic. In this study, we investigate a post-processing approach for cardiac-gated SPECT images by using a 3D residual convolutional neural network (CNN). In our formulation, the network is trained to produce images that are comparable to 4D reconstruction. In the experiments, we demonstrated this approach on a set of 197 clinical acquisitions. The results show that the proposed CNN approach can effectively suppress the noise level in the reconstructed myocardium. It also outperforms two alternative post-processing methods, including a non-local means (NLM) filter previously developed for gated SPECT images.

We propose a patient-specific ("personalized") approach for tailoring the injected activities to individual patients in order to achieve dose reduction in SPECT-myocardial perfusion imaging (MPI). First, we develop a strategy to determine the minimum dose levels required for each patient in a large set of clinical acquisitions (857 subjects) such that the reconstructed images are sufficiently similar to that obtained at conventional clinical dose. We then apply machine learning models to predict the required dose levels on an individual basis based on a set of patient attributes which include body measurements and various clinical variables. We demonstrate the personalized dose models for two commonly used reconstruction methods in clinical SPECT-MPI: 1) conventional filtered backprojection (FBP) with post-filtering and 2) ordered-subsets expectation-maximization (OS-EM) with corrections for attenuation, scatter and resolution, and evaluate their performance in perfusion-defect detection by using the clinical Quantitative Perfusion SPECT software package. The results indicate that the achieved dose reduction can vary greatly among individuals from their conventional clinical dose and that the personalized dose models can achieve further reduction on average compared with a global (non-patient specific) dose reduction approach. In particular, the average personalized dose level can be reduced to 58% and 54% of the full clinical dose, respectively, for FBP and OS-EM reconstruction, while without deteriorating the accuracy in perfusion-defect detection. Furthermore, with the average personalized dose further reduced to only 16% of full dose, OS-EM can still achieve a detection accuracy level comparable to that of FBP with full dose.

A challenging issue in computerized detection of clustered microcalcifications (MCs) is the frequent occurrence of false positives (FPs) caused by local image patterns that resemble MCs. We develop a context-sensitive deep neural network (DNN) for MC detection, aimed to take into account both the local image features of an MC and its surrounding tissue background. The proposed approach was evaluated on the accuracy both in detecting individual MCs and in detecting MC clusters on a set of 292 mammograms using free-response receiver operating characteristic (FROC) analysis. The results demonstrate that the proposed approach could achieve a significantly higher accuracy in detected individual MCs; incorporating image context information in MC detection can be beneficial for reducing FPs.

In this work, we investigate an asymptotically optimal blind zero-bit watermark detector in the wavelet domain. More specifically, assuming that the marginal distribution of detail coefficients is non-Gaussian, we model it with the Student's t probability density function. Furthermore, we assume that the embedding power of the hidden information is unknown, suggesting in this way a new test statistic based on the Rao hypothesis test. The proposed detector exhibits better performance in terms of detection sensitivity and robust properties compared with other known methods in the framework of non-Gaussian environment. Additionally, we investigate a fixed-parameterization approach towards a lightweight detection with regard of time complexity.

Respiratory motion is known to cause non-uniform blur in the reconstructed myocardium in cardiac perfusion imaging with single photon emission computed tomography (SPECT), which can adversely degrade the detectability of perfusion defects. To deal with this issue, we recently proposed a motion-compensated reconstruction scheme by using acquisitions with amplitude-binning. In this study, we evaluate the potential benefit of respiratory motion correction by quantifying the contrast-to-noise ratio (CNR) of the perfusion defects in the reconstructed images using clinical acquisitions. The results demonstrate that with motion correction the CNR is improved to 1.77 from 1.57 (without correction). In addition, there is also an improvement in the spatial resolution of the left ventricular wall. We also investigate the robustness of this reconstruction scheme for reduced dose imaging.

The occurrence of false positives (FPs) varies greatly from case to case in computerized detection of clustered microcalcifications (MCs) from mammogram images. In this work, we explore using a stochastic modeling approach to estimate the number of individual FPs present in a detected MC lesion. We model the spatial occurrence of FPs in the MC detector output by a Poisson spatial point process, of which the parameters are estimated from the detected objects both in the lesion region and in a reference region in the immediate neighborhood of the lesion. We demonstrate the proposed approach on a set of 188 full-field digital mammography images with two existing MC detectors. The results show that on average the error level in the estimated number of FPs is 3.62 when the actual number of FPs is at the level of 11.38 in a detected MC lesion.

In this work, which addresses issues related to the efficient hiding of watermark information in the transform domain, we propose to model the transform coefficients with the Student-t distribution through the multiplicative rule of embedding. Based on the observation that the statistical distribution of the transform coefficients has heavy tailed behavior, we design a new class of watermark detectors following the multiplicative rule of embedding. We present experimental results that compare the proposed method with known state-of-the-art multiplicative watermark detectors and demonstrate its effectiveness in terms of sensitivity and robustness.

Cardiac images in single photon emission computed tomography (SPECT) are known to suffer from loss of resolution associated with respiratory motion. In this work, we investigate the use of a spatially adaptive smoothing prior in a motion-compensated reconstruction framework for SPECT, wherein respiratory binned data are incorporated into the reconstruction of the myocardium with respect to a reference respiratory bin. In the experiments, we evaluated this approach with both simulated imaging data and two sets of clinical acquisitions. The results show that the proposed approach can be effective for improving the heart wall in terms of both the noise level and spatial resolution. The proposed approach was also demonstrated to be robust when the imaging dose was reduced.

Computerized detection of clustered microcalcifications (MCs) in mammograms often suffers from the occurrence of false positives (FPs), which can vary greatly from case to case. We investigate how to apply statistical estimation to determine the number of FPs that are present in a detected MC lesion. First, we describe the number of true positives (TPs) by a Poisson-binomial probability distribution, wherein a logistic regression model is trained to determine the probability for an individual detected MC to be a TP based on its detector output. Afterward, we model the spatial occurrence of FPs in a lesion area by a spatial point process (SPP), of which the distribution parameters are estimated from the detections in the lesion and its surrounding region. Furthermore, to improve the estimation accuracy, we incorporate the Poisson-binomial distribution of the number of TPs into the SPP model using maximum a posteriori estimation. In the experiments, we demonstrated the proposed approach on the detection results from a set of 188 full-field digital mammography (FFDM) images (95 cases) by three existing MC detectors. The results showed that there was a strong consistency between the estimated and the actual number of TPs (or FPs) for these detectors. When the fraction of FPs in detection was varied from 20% to 50%, both the mean and median values of the estimation error were within 11% of the total number of detected MCs in a lesion. In particular, when the number of FPs increased to as high as 11.38 in a cluster on average, the error was 2.51 in the estimated number of FPs. In addition, lesions estimated to be more accurate in detection were shown to have better classification accuracy (for being malignant or benign) than those estimated to be less accurate.

Cardiac single photon emission computed tomography (SPECT) images are known to suffer from both cardiac and respiratory motion blur. In this paper, we investigate a 4-D reconstruction approach to suppress the effect of respiratory motion in gated cardiac SPECT imaging. In this approach, the sequence of cardiac gated images is reconstructed with respect to a reference respiratory amplitude bin in the respiratory cycle. To combat the challenge of inherent high-imaging noise, we utilize the data counts acquired during the entire respiratory cycle by making use of a motion-compensated scheme, in which both cardiac motion and respiratory motion are taken into account. In the experiments, we first use Monte Carlo simulated imaging data, wherein the ground truth is known for quantitative comparison. We then demonstrate the proposed approach on eight sets of clinical acquisitions, in which the subjects exhibit different degrees of respiratory motion blur. The quantitative evaluation results show that the 4-D reconstruction with respiratory correction could effectively reduce the effect of motion blur and lead to a more accurate reconstruction of the myocardium. The mean-squared error of the myocardium is reduced by 22%, and the left ventricle (LV) resolution is improved by 21%. Such improvement is also demonstrated with the clinical acquisitions, where the motion blur is markedly improved in the reconstructed LV wall and blood pool. The proposed approach is also noted to be effective on correcting the spill-over effect in the myocardium from nearby bowel or liver activities.

In diagnostic imaging, recent studies have shown that retrieval of cases that are similar to the case being evaluated can boost its classification performance. In this work we investigate how to improve the utility of the retrieved cases by considering the similarity both in the image features and in the pathology when comparing the cases. To demonstrate the benefit of this retrieval strategy, we propose a boosted Adaboost classifier which can be adapted to the retrieved cases at a low computational cost. The proposed approach was tested on a set of 981 mammogram cases (449 malignant, 532 benign). The results show that the retrieval-boosted Adaboost classifier can significantly outperform its baseline counterpart, and that inclusion of pathology information (measured by the likelihood of malignancy) in the retrieval can further improve the classification accuracy.

In computer-aided diagnosis of clustered microcalcifications (MCs), the individual MCs in a lesion need to be first detected prior to subsequent classification as being benign or malignant. However, owing to noise characteristics and patient variability, the detection accuracy is often adversely compromised by the occurrence of false-positives (FPs) or missed MCs in detection. To deal with difficulty, we propose a case-based decision strategy in MC detection, wherein we model the potential FPs in a detector output by a stochastic neighbor graph, and the MCs are characterized as statistical outliers. In the experiments, we demonstrated this approach on a set of 146 mammograms for two MC detectors. The results show that it could not only reduce the number of FPs (by as much as 39%), but more importantly, it could also reduce case-to-case variability in detection.

Due to the irregularity in respiratory patterns observed clinically, the acquired data in cardiac SPECT with respiratory-gating can exhibit high variability among both gate intervals and acquisition angles. Such variability can lead to differing noise characteristics among respiratory gates, which would adversely affect the accuracy of motion estimation. To address this difficulty, we develop a joint motion-estimation and image-reconstruction approach, in which the respiratory motion is estimated simultaneously along with the source distribution. In the experiments, we demonstrated this joint estimation-reconstruction approach with both quantitative simulated NCAT data and a set of clinical acquisition. We also explored its robustness with reduced imaging dose. The results show that the proposed approach can further improve the reconstructed myocardium over a pre-reconstruction motion-estimation approach.

Mammogram images are now increasingly acquired with full-field digital mammography (FFDM) systems in the clinics. Traditionally, the “for-processing” format of FFDM images is used in computer-aided diagnosis (CAD) of breast cancer. In this study, we investigate the feasibility of using “for-presentation” format of FFDM (which are more readily available) in development of CAD algorithms for microcalcification (MC) lesions. We conduct a quantitative evaluation of both the image features and the detectability of individual MCs on a set of 188 mammograms acquired in both formats. The results demonstrate that there is a high degree of agreement in the image features between the two image formats, and that a slight increase in false-positives in MC detection is observed in for-presentation images.

Due to variability among different subjects, the detection accuracy of microcalcifications (MC) in mammograms often varies greatly from case to case. Even for a well-developed MC detector, its performance can be hampered by a number of factors ranging from imaging noise to inhomogeneity in the breast tissue. To address this issue, we use a Bayes' risk approach to account for the variability in the detector output, wherein the probability model of the false-positives (FPs) is determined directly from the case under consideration. In the experiment, we demonstrated the proposed approach on a set of 408 mammograms. The results show that it could both improve the uniformity in detection accuracy among different cases and reduce the FP rate by as much as 44.16% with true-positive rate at 85%.

Cardiac gated images in single photon emission computed tomography (SPECT) are known to suffer from increased noise due to low data counts. In this work, we investigate a post-filtering approach for SPECT images based on nonlocal means (NLM) filtering. In order to exploit the inherent correlation of the signal components among the different cardiac gates, we employ a spatiotemporal NLM filter, in which both space and temporal neighborhoods are taken into account in the similarity processing. In the experiments, we demonstrated this approach with both simulated NCAT imaging data and a set of clinical acquisition. The results show that the use of temporal smoothing in NLM could be much more effective for improving the quality of gated images than spatial smoothing.

Retrieving and presenting a set of known lesions similar to the one being evaluated has the potential to improve the performance of radiologists in diagnosis of breast cancer with clustered microcalcifications (MCs). In this work, we investigate how perceptually similar cases are related to each other in terms of their image features. We apply supervised learning and feature saliency analysis to determine the most relevant image features based on similarity ratings collected from a group of radiologists on 1,000 image pairs. The results demonstrate that the relevant features are consistent in radiologists' similarity ratings among different lesions, which include geometric clustering features (size and shape) and MC features (size, contrast and shape).

In respiratory-gated cardiac SPECT with amplitude binning, the acquisition time can vary greatly both among respiratory gates and among acquisition angles within each gate. If not properly accounted for, this uneven distribution in acquired data statistics will lead to limited-angle artifacts in reconstruction, which in turn can impact on the accuracy of respiratory motion correction. We investigate a compensation scheme for this uneven distribution by directly taking into account in the imaging model the actual acquisition time at different projection angles. In the experiment, we demonstrated this approach with simulated NCAT imaging data, for which quantitative results were obtained on both the reconstructed myocardium and estimated motion; we also tested the proposed approach on a set of clinical acquisition. The results show that the proposed approach could effectively suppress the limited-angle artifacts and improve the reconstruction in terms of both image accuracy and lesion detectability.

Linear structures are a major contributor to false-positives (FPs) in detection of clustered microcalcifications (MCs) in mammograms. We propose a unified classifier approach to incorporate the dichotomous effect of linear structures in MC detection, the purpose being to suppress the FPs associated with linear structures. We introduce a dummy variable in the classifier model as in traditional regression analysis, the role of which is to adapt the input features to the classifier according to the presence of linear structures. In the experiment we demonstrate the proposed approach by using Adaboost decision stumps as the unified classifier. The results on a set of 200 mammogram images (all containing clustered MCs) show that it could reduce the FPs in an existing SVM detector by up to 47.3% with the true-positive rate at 85%.

Cardiac gated SPECT is an important clinical tool for assessment of both myocardial perfusion and ventricular function. Spatiotemporal (aka 4D) reconstruction has been demonstrated to be effective for suppressing the increased noise in cardiac gated SPECT. In this work, we propose a joint 4D reconstruction approach to accommodate the different respiratory phases in a dual cardiac-respiratory gating scheme in order to combat the artifacts of respiratory motion in cardiac SPECT. The proposed approach is to exploit the correlation in the signal component among both the cardiac and respiratory phases in the acquired data. In our experiments we evaluated the approach using simulated SPECT imaging with the 4D NCAT phantom and Tc-99m labeled Sestamibi as the imaging agent. Our results demonstrate that the proposed approach could effectively suppress the artifacts caused by respiratory motion in the reconstruction.

Linear structures are a major source of false positives (FPs) in computer-aided detection of clustered microcalcifications (MCs) in mammograms. In this work, we investigate whether it is feasible to improve the performance in MC detection by directly exploiting the FPs associated with linear structures. We analyze the cause of FPs by linear structures and their characteristics with an SVM detector, and design a linear structure detection procedure together with a dual-thresholding scheme to separate the linear structures from other tissue background in a mammogram. The proposed procedure was demonstrated on a set of 200 mammograms containing clustered MCs. The results show that it could effectively reduce the FPs in the SVM detector by as much as 30% with the true detection rate at 85%.

We propose a regularization based approach for efficient, case-adaptive classification in computer-aided diagnosis (CAD) of breast cancer. The goal is to boost the classification accuracy on a query case by making use of a set of similar cases retrieved from an existing library of known cases. In the proposed approach, a regularization scheme in the form a prior derived from an existing baseline classifier is used for the adaptive classifier, which can reduce the extra computational burden associated with adaption of the classifier for a query case. We consider two different forms for the regularization prior. In the experiments the proposed approach is demonstrated on a data set of 1,006 clinical cases. The results show that it could achieve improvements in both numerical efficiency and classification performance.

Gated cardiac SPECT imaging suffers from several degrading factors ranging from limited data counts to motion blur. In this work we investigate the use of different optical flow estimation methods for motion-compensated temporal processing in gated SPECT, of which the goal is to improve the accuracy of image reconstruction. In particular, we examine how much room is still left in optical flow estimation toward improving the reconstructed image quality. In our experiments we conducted a quantitative evaluation using simulated imaging study with multiple noise realizations from the NCAT phantom. As an upper bound, the known motion in NCAT was used for reconstruction. The results show that 4D reconstruction with a periodic optical flow model can achieve results almost matching that from the known motion.

This work aims to explore whether we can improve the accuracy of an SVM classifier for microcalcification (MC) detection by incorporating prior knowledge of MCs in mammograms. Based on the fact that MCs are inherently invariant to their spatial orientation in a mammogram, we consider two different techniques for incorporating rotation invariance into SVM, of which one is virtual support vector SVM (VSVM) and the other is tangent vector SVM (TV-SVM). The experiment results show that both techniques can improve the performance in discriminating MCs from the image background, and TV-SVM achieved the best performance. In particular, the sensitivity was 96.3% for TV-SVM, compared to 94.5% for SVM, when the false positive rate was at 0.5%.

In this work, we propose a direct reconstruction approach to determine a sequence of kinetic parametric images from a single gated acquisition, of which the goal is to provide information simultaneously for both tracer kinetics and cardiac wall motion. The parameter images of the different gates are determined jointly using maximum a posteriori (MAP) estimation from all the available image data in order to exploit the similarity among the different gates. The proposed approach is demonstrated in the context of single photon emission computed tomography (SPECT), where the challenge is great due to the under-determined nature of the problem and increased imaging noise. Our results show that use of gated temporal smoothing could effectively improve the reconstruction accuracy of kinetic parameters.

In this work we investigate the use of total variation (TV) regularization in the context of single photon emission computed tomography (SPECT), which is currently widely used for detection and evaluation of coronary artery diseases. Owing to its piecewise smoothing property, TV regularization is known to preserve discontinuities in the resulting images in inverse problems. Our goal is to study whether such a property will be useful for improving the reconstruction accuracy of perfusion defects in cardiac SPECT, which is an important clinical task. In our evaluation study we simulated cardiac gated SPECT imaging with Tc-99m labeled sestamibi. Our results demonstrate that, compared with a traditional quadratic regularization approach, use of TV regularization could lead to improved accuracy of perfect defect detection even when perfection defects are subtle.

Recently we investigated the use of a Fourier harmonic model for determining the optical flow in a periodic image sequence, the goal of which was to exploit the temporal continuity and periodicity in the underlying motion field. In this work, we further develop this optical flow model by incorporating a spatially piecewise smoothness constraint (in the form of total variation) in order to better accommodate the discontinuity of the motion field at an object boundary. In the experiments, we demonstrate its benefits for noise reduction in motion-compensated 4D reconstruction of cardiac gated images. Our results show that it could lead to more accurate reconstruction of the myocardium in spite of strong imaging noise.

In image reconstruction gated acquisition is often used in order to deal with blur caused by organ motion in the resulting images. However, this is achieved almost inevitably at the expense of reduced signal-to-noise ratio in the acquired data. In this work, we propose a reconstruction procedure for gated images based upon use of discrete Fourier transform (DFT) basis functions, wherein the temporal activity at each spatial location is regulated by a Fourier representation. The gated images are then reconstructed through determination of the coefficients of the Fourier representation. We demonstrate this approach in the context of single photon emission computed tomography (SPECT) for cardiac imaging, which is often hampered by the increased noise due to gating and other degrading factors. We explore two different reconstruction algorithms, one is a penalized least-square approach and the other is a maximum a posteriori approach. In our experiments, we conducted a quantitative evaluation of the proposed approach using Monte Carlo simulated SPECT imaging. The results demonstrate that use of DFT-basis functions in gated imaging can improve the accuracy of the reconstruction. As a preliminary demonstration, we also tested this approach on a set of clinical acquisition.

In this work we propose an image-retrieval based approach for case-adaptive classifier design in computer-aided diagnosis (CAD). The traditional approach in CAD is to first train a pattern-classifier based on a set of existing training samples, and then apply this classifier to subsequent new cases. In our proposed approach, we will first apply image-retrieval to obtain a set of lesion images from a library of known cases that have similar image features to a case being diagnosed (i.e., query). These retrieved cases are then used to optimize a pattern-classifier toward boosting its classification accuracy on the query case. In our experiments the proposed retrieval-driven approach was tested on a library of mammogram images from 589 cases (331 benign, 258 malignant), and was demonstrated to yield significant improvement in classification performance.

In this work we develop a fully five-dimensional (5D) reconstruction approach based on B-spline modeling for cardiac gated dynamic images. The goal is to obtain a single sequence showing simultaneously both cardiac motion and kinetic tracer distribution change over time from one acquisition. The proposed approach is demonstrated in the context of single photon emission computed tomography (SPECT), where the challenge is great due to the under-determined nature of the problem and increased imaging noise. Our evaluation results demonstrate that the 5D reconstruction procedure can lead to accurate reconstruction of gated dynamic images for both cardiac motion and perfusion defect detection.

Prostate cancer is a leading cause of cancer death for men in the United States. Fortunately, the survival rate for early diagnosed patients is relatively high. Therefore, in vivo imaging plays an important role for the detection and treatment of the disease. Accurate prostate cancer localization with noninvasive imaging can be used to guide biopsy, radiotherapy, and surgery as well as to monitor disease progression. Magnetic resonance imaging (MRI) performed with an endorectal coil provides higher prostate cancer localization accuracy, when compared to transrectal ultrasound (TRUS). However, in general, a single type of MRI is not sufficient for reliable tumor localization. As an alternative, multispectral MRI, i.e., the use of multiple MRI-derived datasets, has emerged as a promising noninvasive imaging technique for the localization of prostate cancer; however almost all studies are with human readers. There is a significant inter and intraobserver variability for human readers, and it is substantially difficult for humans to analyze the large dataset of multispectral MRI. To solve these problems, this study presents an automated localization method using cost-sensitive support vector machines (SVMs) and shows that this method results in improved localization accuracy than classical SVM. Additionally, we develop a new segmentation method by combining conditional random fields (CRF) with a cost-sensitive framework and show that our method further improves cost-sensitive SVM results by incorporating spatial information. We test SVM, cost-sensitive SVM, and the proposed cost-sensitive CRF on multispectral MRI datasets acquired from 21 biopsy-confirmed cancer patients. Our results show that multispectral MRI helps to increase the accuracy of prostate cancer localization when compared to single MR images; and that using advanced methods such as cost-sensitive SVM as well as the proposed cost-sensitive CRF can boost the performance significantly when compared to SVM.

We propose a temporal modeling approach for determining image motion from a sequence of images wherein the inherent motion is periodic over time. To exploit the periodic nature of the motion, we use a Fourier harmonic representation to model the temporal evolution of the motion field for the entire sequence. We then determine the motion field simultaneously for the different image frames by estimating the parameters of this representation model, where the model order in the Fourier representation serves as a regularization parameter on the temporal coherence of the motion field. This approach can take advantage of the statistics of all the available data in the image sequence. In our experiments, we tested the proposed approach on several motion types at different noise levels, including translational motion, convergent/divergent motion, and cardiac motion. Our results demonstrate that this approach could lead to more robust estimation of the motion field in the presence of strong imaging noise compared to a frame-by-frame estimation approach.

We propose a spatial point-process modeling approach to improve the detection of clustered microcalcifications (MCs) in mammogram images. Apart from the predominant approach for MC detection, in which individual MCs in an image are first detected independently and then grouped into clusters, our proposed approach aims to incorporate the spatial clustering property of the MCs directly into the detection process (i.e., MCs tend to appear in small clusters). We model the MCs by a marked point process (MPP) in which spatially neighboring MCs are interactive with each other. The detection is achieved through maximum a posteriori (MAP) estimation of the parameters of the MPP model. The proposed approach was evaluated with a dataset of 141 clinical mammograms, and the results show that it could yield improved performance compared with a recently proposed SVM detector.

In our previous work we proposed a dynamic image reconstruction procedure for gated cardiac imaging, of which the goal is to obtain a single image sequence that shows simultaneously both cardiac motion and tracer distribution change over time. In this work, we further develop and demonstrate the feasibility of this procedure for perfusion defect detection in gated cardiac imaging. We conduct Fisher's linear discriminant analysis on the reconstructed dynamic images, and derive quantitative measures to differentiate defects from normal myocardial perfusion. Results are presented to demonstrate the proposed development using simulated gated cardiac imaging with the NURBS-based cardiac-torso (NCAT) phantom.

Breast cancer is the second-most common and leading cause of cancer death among women. It has become a major health issue in the world over the past 50 years, and its incidence has increased in recent years. Early detection is an effective way to diagnose and manage breast cancer. Computer-aided detection or diagnosis (CAD) systems can play a key role in the early detection of breast cancer and can reduce the death rate among women with breast cancer. The purpose of this paper is to provide an overview of recent advances in the development of CAD systems and related techniques. We begin with a brief introduction to some basic concepts related to breast cancer detection and diagnosis. We then focus on key CAD techniques developed recently for breast cancer, including detection of calcifications, detection of masses, detection of architectural distortion, detection of bilateral asymmetry, image enhancement, and image retrieval.

It is now widely accepted that image quality should be evaluated using task-based criteria, such as human-observer performance in a lesion-detection task. The channelized Hotelling observer (CHO) has been widely used as a surrogate for human observers in evaluating lesion detectability. In this paper, we propose that the problem of developing a numerical observer can be viewed as a system-identification or supervised-learning problem, in which the goal is to identify the unknown system of the human observer. Following this approach, we explore the possibility of replacing the Hotelling detector within the CHO with an algorithm that learns the relationship between measured channel features and human observer scores. Specifically, we develop a channelized support vector machine (CSVM) which we compare to the CHO in terms of its ability to predict human-observer performance. In the examples studied, we find that the CSVM is better able to generalize to unseen images than the CHO, and therefore may represent a useful improvement on the CHO methodology, while retaining its essential features.

Prostate cancer is one of the leading causes of death from cancer among men in the United States. Currently, high-resolution magnetic resonance imaging (MRI) has been shown to have higher accuracy than trans-rectal ultrasound (TRUS) when used to ascertain the presence of prostate cancer. As MRI can provide both morphological and functional images for a tissue of interest, some researchers are exploring the uses of multispectral MRI to guide prostate biopsies and radiation therapy. However, success with prostate cancer localization based on current imaging methods has been limited due to overlap in feature space of benign and malignant tissues using any one MRI method and the interobserver variability. In this paper, we present a new unsupervised segmentation method for prostate cancer detection, using fuzzy Markov random fields (fuzzy MRFs) for the segmentation of multispectral MR prostate images. Typically, both hard and fuzzy MRF models have two groups of parameters to be estimated: the MRF parameters and class parameters for each pixel in the image. To date, these two parameters have been treated separately, and estimated in an alternating fashion. In this paper, we develop a new method to estimate the parameters defining the Markovian distribution of the measured data, while performing the data clustering simultaneously. We perform computer simulations on synthetic test images and multispectral MR prostate datasets to demonstrate the efficacy and efficiency of the proposed method and also provide a comparison with some of the commonly used methods.

We propose a temporal modeling approach for determining image motion from a sequence of images within which the inherent motion is periodic. To exploit the periodic nature of the motion, we use a Fourier harmonic representation to model the motion field for the entire sequence. We then determine the motion field by estimating the parameters of this representation model. This joint estimation approach can take advantage of the statistics of all the available data in the image sequence. In our experiments, we applied the proposed approach to estimate the cardiac motion in gated cardiac SPECT perfusion images. Our results demonstrate that it could achieve robust estimation in the presence of strong imaging noise.

In cardiac imaging the data acquisition is often gated according to the ECG signal at the expense of signal to noise ratio in order to deal with cardiac motion. In this work, we propose a spatio-temporal reconstruction procedure by using a Fourier harmonic representation model for the temporal image activities. To further combat the increased imaging noise, we also include a spatial smoothing prior into the reconstruction process. We then reconstruct the different harmonics in the representation model by using both a penalized least-squares approach and a maximum a posteriori approach. In our experiments, the proposed approach was demonstrated using simulated cardiac SPECT perfusion imaging based on the NURBS-based cardiac-torso (NCAT) phantom.

In this paper we aim to develop a computationally-efficient image-segmentation procedure for detection and quantification of soft plaques in coronary arteries from multidetector CT images. The proposed method consists of three steps: extraction of the arterial lumen centerline, segmentation of the lumen and arterial wall based on a locally-adaptive mixture-model using the expectation- maximization algorithm, and detection of soft plaques based on effective cross-sectional areas of the lumen and of the wall. Preliminary results using clinical acquisitions are presented to demonstrate the effectiveness of the proposed method.

We propose a four-dimensional reconstruction method for noise reduction in gated cardiac SPECT images. Aiming to exploit the periodic nature of cardiac motion, we use a Fourier harmonic representation to model the image activities along the gated temporal dimension. We develop a penalized least-squares approach to reconstruct the different harmonics in the representation model, which also takes into account spatial smoothing. The proposed method is demonstrated using simulated cardiac perfusion imaging based on the NURBS-based cardiac-torso (NCAT) phantom. Our results show that it could lead to improved reconstruction of the gated images.

In this paper, we propose a new family of watermark detectors for additive watermarks in digital images. These detectors are based on a recently proposed hierarchical, two-level image model, which was found to be beneficial for image recovery problems. The top level of this model is defined to exploit the spatially varying local statistics of the image, while the bottom level is used to characterize the image variations along two principal directions. Based on this model, we derive a class of detectors for the additive watermark detection problem, which include a generalized likelihood ratio, Bayesian, and Rao test detectors. We also propose methods to estimate the necessary parameters for these detectors. Our numerical experiments demonstrate that these new detectors can lead to superior performance to several state-of-the-art detectors.

Temporal basis functions have been found to be effective for regularizing the time-varying image activities in dynamic emission tomography. By modelling the tracer distribution function at individual pixels as a linear combination of a set of basis functions, the reconstruction problem becomes that of estimating the weights of the basis functions. In this work, we explore the use of temporally adaptive regularization in the basis function domain, where spatial smoothing is enforced in an adaptive fashion according to the time-varying data statistics. In our experiments the proposed method was demonstrated using simulated Tc99m-Teboroxime SPECT imaging with the gated mathematical cardiac-torso (gMCAT) phantom. Our results show that the proposed approach can lead to more accurate reconstruction of the time activities, which is important for differentiation between a perfusion defect and the normal myocardium.

In this paper we propose a new family of watermark detectors for additive watermarks in digital images. These detectors are based on a recently proposed two-level, hierarchical image model, which was found to be beneficial for image recovery problems. The top level of this model is defined to exploit the spatially-varying local statistics of the image, while the bottom level is used to characterize the image variations along two principal directions. Based on this model we derive a class of detectors for the additive watermark detection problem, including the generalized likelihood ratio test (GLRT) and Rao detectors.

In this paper we propose a microcalcification classification scheme, assisted by content-based mammogram retrieval, for breast cancer diagnosis. We recently developed a machine learning approach for mammogram retrieval where the similarity measure between two lesion mammograms is modeled after expert observers. In this work we investigate how to use retrieved similar cases as references to improve the performance of a numerical classifier. Our rationale is that by adap-tively incorporating local proximity information into a classifier, it can help improve its classification accuracy, thereby leading to an improved "second opinion" to radiologists. Our experimental results on a mammogram database demonstrate that the proposed retrieval-driven approach with an adaptive support vector machine (SVM) could improve the classification performance from 0.78 to 0.82 in terms of the area under the ROC curve.

In this paper we present new detectors for additive watermarks when the power of the watermark is unknown. These detectors are based on modeling the image using student-t statistics. As a result, due to the generative properties of the student-t density function, such models are spatially adaptive and the Expectation-Maximization algorithm can be used to obtain maximum likelihood estimates of their parameters. Using these image models detectors based on the generalized likelihood ratio and Rao tests are derived for this problem. Numerical experiments are presented that demonstrate the properties of these detectors and compared them with previously proposed detectors.

In this paper, we propose an approach for the reconstruction of dynamic images from a gated cardiac data acquisition. The goal is to obtain an image sequence that can show simultaneously both cardiac motion and time-varying image activities. To account for the cardiac motion, the cardiac cycle is divided into a number of gate intervals, and a time-varying image function is reconstructed for each gate. In addition, to cope with the under-determined nature of the problem, the time evolution at each pixel is modeled by a B-spline function. The dynamic images for the different gates are then jointly determined using maximum a posteriori estimation, in which a motion-compensated smoothing prior is introduced to exploit the similarity among the different gates. The proposed algorithm is evaluated using a dynamic version of the 4-D gated mathematical cardiac torso phantom simulating a gated single photon emission computed tomography perfusion acquisition with Technitium-99m labeled Teboroxime. We thoroughly evaluated the performance of the proposed algorithm using several quantitative measures, including signal-to-noise ratio analysis, bias-variance plot, and time activity curves. Our results demonstrate that the proposed joint reconstruction approach can improve significantly the accuracy of the reconstruction.

We propose an approach to analyzing functional neuroimages in which 1) regions of neuronal activation are described by a superposition of spatial kernel functions, the parameters of which are estimated from the data and 2) the presence of activation is detected by means of a generalized likelihood ratio test (GLRT). Kernel methods have become a staple of modern machine learning. Herein, we show that these techniques show promise for neuroimage analysis. In an on-off design, we model the spatial activation pattern as a sum of an unknown number of kernel functions of unknown location, amplitude, and/or size. We employ two Bayesian methods of estimating the kernel functions. The first is a maximum a posteriori (MAP) estimation method based on a Reversible-Jump Markov-chain Monte-Carlo (RJMCMC) algorithm that searches for both the appropriate model complexity and parameter values. The second is a relevance vector machine (RVM), a kernel machine that is known to be effective in controlling model complexity (and thus discouraging overfitting). In each method, after estimating the activation pattern, we test for local activation using a GLRT. We evaluate the results using receiver operating characteristic (ROC) curves for simulated neuroimaging data and example results for real fMRI data. We find that, while RVM and RJMCMC both produce good results, RVM requires far less computation time, and thus appears to be the more promising of the two approaches.

It has been previously observed that independent component analysis (ICA), if applied to data pooled in a particular way, may lessen the need for spatial alignment of scans in a functional neuroimaging study. In this paper, we seek to determine analytically the conditions under which this observation is true, not only for spatial ICA, but also for temporal ICA and for principal component analysis (PCA). In each case, we find conditions that the spatial alignment operator must satisfy to ensure invariance of the results. We illustrate our findings using functional magnetic-resonance imaging (fMRI) data. Our analysis is applicable to both intersubject and intrasubject spatial normalization.

A key in content-based image retrieval is the definition of similarity measure for comparing a query image with images in a database. In this work, we explore a similarity measure based on supervised learning from expert readers for mammogram retrieval. We evaluate the approach using an observer study with a set of clinical mammograms. Our results demonstrate that the proposed supervised learning approach can be used to model the notion of similarity by expert readers in their interpretation of mammogram images, and can outperform alternative similarity measures derived from unsupervised learning.

In this work, we propose an image reconstruction procedure which will unify gated SPECT and dynamic SPECT into a single imaging method. Traditionally, gated SPECT and dynamic SPECT are treated as two distinct directions in SPECT imaging: gated SPECT aims to reconstruct a periodic stationary sequence of the cardiac cycle, while dynamic SPECT aims to obtain a time-varying distribution of the radiolabeled tracer during the study. In the proposed reconstruction procedure, we divide the cardiac cycle into a number of gate intervals as in gated SPECT, but treat the tracer distribution for each gate as a time-varying signal. By using list-mode data, this procedure produces an image sequence that shows both cardiac motion and time-varying tracer distribution. To demonstrate the proposed method, we simulated gated cardiac perfusion imaging with Tc-99m labeled Teboroxime using the 4D gated mathematical cardiac-torso (gMCAT) phantom. Preliminary results are presented to demonstrate the feasibility of the proposed approach.

Accurate detection of microcalcification (MC) clusters is an important problem in breast cancer diagnosis. In this paper, we propose the use of a recently developed machine learning technique - relevance vector machine (RVM) - for automatic detection of MCs in digitized mammograms. RVM is based on Bayesian estimation theory, and as a feature it can yield a decision function that depends on only a very small number of so-called relevance vectors. The proposed method is tested using a database of 141 clinical mammograms, and compared with a support vector machine (SVM) classifier, which we developed previously. It is demonstrated that the RVM classifier achieves essentially the same detection performance as the SVM classifier, but does so with a much sparser kernel representation. Consequently, the RVM classifier greatly reduces the computational complexity, making it more suitable for real-time implementation.

In this paper, we investigate several state-of-the-art machine-learning methods for automated classification of clustered microcalcifications (MCs). The classifier is part of a computer-aided diagnosis (CADx) scheme that is aimed to assisting radiologists in making more accurate diagnoses of breast cancer on mammograms. The methods we considered were: support vector machine (SVM), kernel Fisher discriminant (KFD), relevance vector machine (RVM), and committee machines (ensemble averaging and AdaBoost), of which most have been developed recently in statistical learning theory. We formulated differentiation of malignant from benign MCs as a supervised learning problem, and applied these learning methods to develop the classification algorithm. As input, these methods used image features automatically extracted from clustered MCs. We tested these methods using a database of 697 clinical mammograms from 386 cases, which included a wide spectrum of difficult-to-classify cases. We analyzed the distribution of the cases in this database using the multidimensional scaling technique, which reveals that in the feature space the malignant cases are not trivially separable from the benign ones. We used receiver operating characteristic (ROC) analysis to evaluate and to compare classification performance by the different methods. In addition, we also investigated how to combine information from multiple-view mammograms of the same case so that the best decision can be made by a classifier. In our experiments, the kernel-based methods (i.e., SVM, KFD, and RVM) yielded the best performance (Az = 0.85, SVM), significantly outperforming a well-established, clinically-proven CADx approach that is based on neural network (Az = 0.80).

Clustered microcalcifications (MC) in mammograms can be an important early sign of breast cancer in women. Their accurate detection is important in computer-aided detection (CADe). In this paper, we propose the use of a recently developed machine-learning technique--relevance vector machine (RVM)--for detection of MCs in digital mammograms. RVM is based on Bayesian estimation theory, of which a distinctive feature is that it can yield a sparse decision function that is defined by only a very small number of so-called relevance vectors. By exploiting this sparse property of the RVM, we develop computerized detection algorithms that are not only accurate but also computationally efficient for MC detection in mammograms. We formulate MC detection as a supervised-learning problem, and apply RVM as a classifier to determine at each location in the mammogram if an MC object is present or not. To increase the computation speed further, we develop a two-stage classification network, in which a computationally much simpler linear RVM classifier is applied first to quickly eliminate the overwhelming majority, non-MC pixels in a mammogram from any further consideration. The proposed method is evaluated using a database of 141 clinical mammograms (all containing MCs), and compared with a well-tested support vector machine (SVM) classifier. The detection performance is evaluated using free-response receiver operating characteristic (FROC) curves. It is demonstrated in our experiments that the RVM classifier could greatly reduce the computational complexity of the SVM while maintaining its best detection accuracy. In particular, the two-stage RVM approach could reduce the detection time from 250 s for SVM to 7.26 s for a mammogram (nearly 35-fold reduction). Thus, the proposed RVM classifier is more advantageous for real-time processing of MC clusters in mammograms.

In this work we explore the use of a content-adaptive mesh model for image compression. We first model the image to be compressed by a quadtree mesh representation, in which the nodal values are determined using a least squares fit. The resulting mesh structure is coded using a 4-ary tree and the mesh nodal values are coded using a hierarchical predictive coding scheme. Our experimental results demonstrate that the proposed approach can achieve good compression performance and can significantly outperform JPEG both subjectively and objectively in low bit-rate applications.

In this paper, we explore the use of a content-adaptive mesh model (CAMM) for tomographic image reconstruction. In the proposed framework, the image to be reconstructed is first represented by a mesh model, an efficient image description based on nonuniform sampling. In the CAMM, image samples (represented as mesh nodes) are placed most densely in image regions having fine detail. Tomographic image reconstruction in the mesh domain is performed by maximum-likelihood (ML) or maximum a posteriori (MAP) estimation of the nodal values from the measured data. A CAMM greatly reduces the number of unknown parameters to be determined, leading to improved image quality and reduced computation time. We demonstrated the method in our experiments using simulated gated single photon emission computed tomography (SPECT) cardiac-perfusion images. A channelized Hotelling observer (CHO) was used to evaluate the detectability of perfusion defects in the reconstructed images, a task-based measure of image quality. A minimum description length (MDL) criterion was also used to evaluate the effect of the representation size. In our application, both MDL and CHO suggested that the optimal number of mesh nodes is roughly five to seven times smaller than the number of projection bins. When compared to several commonly used methods for image reconstruction, the proposed approach achieved the best performance, in terms of defect detection and computation time. The research described in this paper establishes a foundation for future development of a (four-dimensional) space-time reconstruction framework for image sequences in which a built-in deformable mesh model is used to track the image motion.

In this paper, we describe an approach to content-based retrieval of medical images from a database, and provide a preliminary demonstration of our approach as applied to retrieval of digital mammograms. Content-based image retrieval (CBIR) refers to the retrieval of images from a database using information derived from the images themselves, rather than solely from accompanying text indices. In the medical-imaging context, the ultimate aim of CBIR is to provide radiologists with a diagnostic aid in the form of a display of relevant past cases, along with proven pathology and other suitable information. CBIR may also be useful as a training tool for medical students and residents. The goal of information retrieval is to recall from a database information that is relevant to the user's query. The most challenging aspect of CBIR is the definition of relevance (similarity), which is used to guide the retrieval machine. In this paper, we pursue a new approach, in which similarity is learned from training examples provided by human observers. Specifically, we explore the use of neural networks and support vector machines to predict the user's notion of similarity. Within this framework we propose using a hierarchal learning approach, which consists of a cascade of a binary classifier and a regression module to optimize retrieval effectiveness and efficiency. We also explore how to incorporate online human interaction to achieve relevance feedback in this learning framework. Our experiments are based on a database consisting of 76 mammograms, all of which contain clustered microcalcifications (MCs). Our goal is to retrieve mammogram images containing similar MC clusters to that in a query. The performance of the retrieval system is evaluated using precision-recall curves computed using a cross-validation procedure. Our experimental results demonstrate that: 1) the learning framework can accurately predict the perceptual similarity reported by human observers, thereby serving as a basis for CBIR; 2) the learning-based framework can significantly outperform a simple distance-based similarity metric; 3) the use of the hierarchical two-stage network can improve retrieval performance; and 4) relevance feedback can be effectively incorporated into this learning framework to achieve improvement in retrieval precision based on online interaction with users; and 5) the retrieved images by the network can have predicting value for the disease condition of the query.

In this work we explore the use of a content-adaptive mesh model (CAMM) in the classical problem of image restoration. In the proposed framework, we first model the image to be restored by an efficient mesh representation. A CAMM can be viewed as a form of image representation using nonuniform samples, of which the mesh nodes (i.e., image samples) are adaptively placed according to the local content of the image. The image is then restored through estimating the model parameters (i.e., mesh nodal values) from the data. A CAMM provides a natural spatially-adaptive regularization mechanism for image restoration in that the interpolation basis functions in a CAMM have their spatial support varying with the local image content. We present some exploratory results to demonstrate the proposed approach.

In this work we present a fast procedure for content-adaptive mesh representation of vector-valued (e.g., color) images. The goal is to obtain a single mesh structure that accurately represents all the individual components of the image. The proposed method is justified by an error bound that is rigorously derived for such a representation. It employs an error-diffusion type algorithm to place the mesh nodes nonuniformly in the image domain according to the image content. Experimental results demonstrate that: (1) a compact and accurate representation for color images can be achieved at low computational cost by the proposed algorithm; and (2) joint treatment of the different image components by the proposed algorithm can result in a more accurate mesh representation than a mesh based on a single image component (such as intensity) alone.

In this work we explore a new technique for relevance feedback in a learning-based framework for retrieval of relevant mammogram images from a database, for purposes of aiding diagnoses. Our goal is to adapt online the learning procedure in accordance with user responses without the need to repeat the training procedure. Toward this end we develop a relevance feedback approach based on the concept of incremental learning developed recently in the theory of support vector machines. The proposed approach is demonstrated using clustered microcalcifications extracted from a database consisting of 76 mammograms.

In this paper we study a motion-compensated approach for simultaneous reconstruction of image frames in a time sequence. We treat the frames in a sequence collectively as a single function of both space and time, and define a temporal prior to account for the temporal correlations in a sequence. This temporal prior is defined in a form of motion-compensation, aimed to follow the curved trajectories of the object motion through space-time. The image frames are then obtained through estimation using the expectation-maximization (EM) algorithm. The proposed algorithm was evaluated extensively using the 4D gated mathematical cardiac-torso (gMCAT) Dl.Ql phantom to simulate gated SPECT perfusion imaging with Tc99m. Our experimental results demonstrate that the use of motion compensation for reconstruction can lead to significant improvement in image quality and reconstruction accuracy.

Mesh modeling is an important problem with many applications in image processing. A key issue in mesh modeling is how to generate a mesh structure that well represents an image by adapting to its content. We propose a new approach to mesh generation, which is based on a theoretical result derived on the error bound of a mesh representation. In the proposed method, the classical Floyd-Steinberg error-diffusion algorithm is employed to place mesh nodes in the image domain so that their spatial density varies according to the local image content. Delaunay triangulation is next applied to connect the mesh nodes. The result of this approach is that fine mesh elements are placed automatically in regions of the image containing high-frequency features while coarse mesh elements are used to represent smooth areas. The proposed algorithm is noniterative, fast, and easy to implement. Numerical results demonstrate that, at very low computational cost, the proposed approach can produce mesh representations that are more accurate than those produced by several existing methods. Moreover, it is demonstrated that the proposed algorithm performs well with images of various kinds, even in the presence of noise.

In this paper we present a new approach for clustering data. The clustering metric used is the normalized cross-correlation, also known as similarity, instead of the traditionally used Euclidean distance. The main advantage of this metric is that it depends on the signal shape rather than its amplitude. Under an assumption of an exponential probability model that has several desirable properties, the expectation-maximization (EM) framework is used to derive two iterative clustering algorithms. Numerical experiments are presented using simulated data in a dynamic positron emission topography study of the brain. Initial results demonstrate that the proposed method achieves better performance than several existing clustering methods.

We propose the use of a content-adaptive volumetric mesh model for fully three-dimensional (3D) tomographic image reconstruction. In the proposed framework, the image to be reconstructed is first modeled by an efficient mesh representation. The image is then obtained through estimation of the nodal values from the measured data. The use of a mesh representation can alleviate the ill-posed nature of the reconstruction problem, thereby leading to improved quality in the reconstructed images. In addition, it reduces the data storage requirement, resulting in efficient algorithms. The proposed methods are tested using gated cardiac-perfusion images. Initial results demonstrate that the proposed approach achieves good performance when compared to several commonly used methods for image reconstruction, and produces results very rapidly.

In this work we present a fast, content-adaptive approach for three-dimensional (3D) mesh representation of volumetric images. A rigorous error bound is derived for a 3D mesh representation of a volumetric image based on the theory of function interpolation. From this result, a computationally efficient algorithm is proposed for adaptive placement of mesh nodes (hence mesh elements) in the 3D image domain according to the image content. Experimental results demonstrate that a highly compact and accurate representation of volumetric images can be achieved at low computational cost by the proposed algorithm.

While geometric attacks are one of the most challenging problems in watermarking, random bending is probably the most difficult to handle among all geometric attacks. We present a watermarking scheme based on a new deformable mesh model to combat such attacks. The distortion is corrected using the distortion field (DF) estimated by minimizing the matching error between the meshes of the original and the attacked image. A CDMA watermarking method is used for testing the proposed method, which embeds a multi-bit signature in the DCT domain and uses mesh model correction to achieve robustness. Experiments show that the proposed scheme can survive a wide range of random bending attacks.

In this work, we explore the use of a learning-based framework for retrieval of relevant mammogram images from a database, for purposes of aiding diagnoses. A fundamental issue is how to characterize the notion of similarity between images for use in assessing relevance of images in the database. We investigate the use of several learning algorithms, namely, neural networks and support vector machines, in a two-stage hierarchical learning network for predicting the perceptual similarity from similarity scores collected in human-observer studies. The proposed approach is demonstrated using microcalcification clusters extracted from a database consisting of 76 mammograms. Initial results demonstrate that the proposed two-stage hierarchical learning network outperforms a single-stage learning network.

Microcalcification (MC) clusters in mammograms can be an indicator of breast cancer. We propose, for the first time, the use of support vector machine (SVM) learning for automated detection of MCs in digitized mammograms. In the proposed framework, MC detection is formulated as a supervised-learning problem and the method of SVM is employed to develop the detection algorithm. The proposed method is developed and evaluated using a database of 76 mammograms containing 1120 MCs. To evaluate detection performance, free-response receiver operating characteristic (FROC) curves are used. Experimental results demonstrate that, when compared to several other existing methods, the proposed SVM framework offers the best performance.

We propose a new signal-detection approach for detecting brain activations from PET or fMRI images in a two-state ("on-off") neuroimaging study. We model the activation pattern as a superposition of an unknown number of circular spatial basis functions of unknown position, size, and amplitude. We determine the number of these functions and their parameters by maximum a posteriori (MAP) estimation. To maximize the posterior distribution we use a reversible jump Markov-chain Monte-Carlo (RJMCMC) algorithm. The main advantage of RJMCMC is that it can estimate parameter vectors of unknown length. Thus, in the model used the number of activation sites does not need to be known. Using a phantom derived from a neuroimaging study, we demonstrate that the proposed method can estimate more accurately the activation pattern from traditional approaches.

In this paper, we investigate an approach based on support vector machines (SVMs) for detection of microcalcification (MC) clusters in digital mammograms, and propose a successive enhancement learning scheme for improved performance. SVM is a machine-learning method, based on the principle of structural risk minimization, which performs well when applied to data outside the training set. We formulate MC detection as a supervised-learning problem and apply SVM to develop the detection algorithm. We use the SVM to detect at each location in the image whether an MC is present or not. We tested the proposed method using a database of 76 clinical mammograms containing 1120 MCs. We use free-response receiver operating characteristic curves to evaluate detection performance, and compare the proposed algorithm with several existing methods. In our experiments, the proposed SVM framework outperformed all the other methods tested. In particular, a sensitivity as high as 94% was achieved by the SVM method at an error rate of one false-positive cluster per image. The ability of SVM to out perform several well-known methods developed for the widely studied problem of MC detection suggests that SVM is a promising technique for object detection in a medical imaging application.

A new technique for designing digital all-pass IIR filters is proposed. The approach is based on the vector space projection method. Constraint sets, and their associated projectors, that capture the properties of the desired group delay are given. Examples that demonstrate the advantages and flexibility of this method as well as comparisons with a well-known method (Nguyen et al., 1994) are furnished.

We propose the use of a content-adaptive mesh model (CAMM) for tomographic image reconstruction. In the proposed framework, the image to be reconstructed is first modeled by an efficient mesh representation. The image is then obtained through estimation of the nodal values from the measured data. The use of a CAMM can greatly alleviate the ill-posed nature of the reconstruction problem, thereby leading to improved quality in the reconstructed images. In addition, it can lead to development of efficient numerical reconstruction algorithms. Finally, it can be useful for motion-tracking of image sequences. The proposed methods are tested using simulated gated cardiac-perfusion SPECT images. Our results indicate that, among the methods tested, the proposed approach achieves the best performance in terms of image quality and computation time, and can also reduce the memory requirement.

Previously, we proposed a computationally efficient approach to content-adaptive mesh generation used for image representation (see Lee, J. et al., IEEE Int. Conf. Image Proc., 2000). We now provide a theoretical basis for that method, which leads to an improved version of the algorithm. An error bound is derived for a mesh representation of an image based on the theory of function interpolation. From this result, a more accurate scheme is proposed for placement of mesh elements in the image domain according to the image content. Experimental results, compared to other methods, show that a highly accurate image representation can be obtained at extremely low computational cost by the proposed technique.

We explore the use of various learning algorithms to predict the user's measure of similarity between a given query image and images in a database. Our aim is to obtain a similarity coefficient, for use in image retrieval, that more accurately reflects that of the user. The performance of a variety of learning machines was evaluated using statistical resampling to estimate the prediction error and retrieval effectiveness. The proposed approach was demonstrated using synthetic shape and texture examples. The results of the study are very promising, especially those obtained by the general regression neural network and the support vector machine/radial basis function method.

A new, effective approach is proposed for content-adaptive mesh generation used for image representation. The proposed approach employs the Floyd-Steinberg (1975) method, a classical error-diffusion algorithm for image halftoning, to distribute the mesh nodes in the domain of an image based on its gradient magnitude. Consequently, fine mesh elements are placed automatically in regions of the image containing high-frequency features while coarse mesh elements are used in smooth regions. The proposed algorithm is non-iterative and easy to implement. Numerical results demonstrate that it can yield a compact, accurate representation of images.

We present some new results for multichannel recovery of compressed video. This work extends our previously proposed multichannel recovery algorithm in that: (1) it allows bi-directional motion information to be utilised in the recovery algorithm and the motion compensation can be done at a sub-pixel level; (2) a simplified version of the recovery algorithm is introduced to reduce the computational cost. Numerical simulations using H.261 and H.263 compressed video sequences are provided to demonstrate the effectiveness of the proposed algorithms.

In this study we propose a multichannel recovery approach to ameliorating artifacts in compressed video. According to this approach, regularization operators are defined to capture both spatial and temporal correlation properties in an image sequence. In particular a regularization operator is defined explicitly to enforce smoothness along the motion trajectories. In addition, a new approach is proposed for the determination of regularization parameters in the recovery algorithm utilizing the original image in the coder, unlike in traditional image restoration where they have to be estimated from the already degraded image data.

We present a new image recovery algorithm to remove, in addition to blocking, ringing artifacts from compressed images and video. This new algorithm is based on the theory of projections onto convex sets (POCS). A new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure. The definition of these smoothness sets also takes into account the fact that the visibility of compression artifacts in an image is spatially varying. To overcome the numerical difficulty in computing the projections onto these sets, a divide-and-conquer (DAC) strategy is introduced. According to this strategy, new smoothness sets are derived such that their projections are easier to compute. The effectiveness of the proposed algorithm is demonstrated through numerical experiments using Motion Picture Expert Group based (MPEG-based) coders-decoders (codecs).

At the present time, block-transform coding is probably the most popular approach for image compression. For this approach, the compressed images are decoded using only the transmitted transform data. We formulate image decoding as an image recovery problem. According to this approach, the decoded image is reconstructed using not only the transmitted data but, in addition, the prior knowledge that images before compression do not display between-block discontinuities. A spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets. Apart from the data constraint set, this algorithm uses another new constraint set that enforces between-block smoothness. The novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics. A simplified spatially adaptive recovery algorithm is also proposed, and the analysis of its computational complexity is presented. Numerical experiments are shown that demonstrate that the proposed algorithms work better than both the JPEG deblocking recommendation and our previous projection-based image decoding approach.

In this paper we present a new non-linear image recovery algorithm which is based on the theory of projections onto convex sets (POCS) to reconstruct compressed images. We introduce a new family of convex smoothness constraint sets. These sets are based on the concept of the line process which models explicitly the edge structure of images and thus can eliminate both ringing and blocking coding artifacts. We also introduce a divide-and-conquer (DAC) strategy to compute the projections onto the new smoothness sets efficiently. Finally, we present experiments that demonstrate the effectiveness of the new smoothness constraint sets.>

We present a gradient-projection algorithm for solving the classical blind deconvolution problem. In our approach all known a priori information about both the unknown source and blurring functions is expressed via constraint sets. In computer simulations, the algorithm performed well even when the prior information was not accurate. In this study the algorithm is also compared with a conjugate gradient algorithm proposed by Lane (see J. Opt. Soc. Am. A, vol.9, no.9, p.1508-1514, 1992).>

In most block-transform based codecs (coder-decoder) the compressed image is reconstructed using only the transmitted data. In this paper, the reconstruction is formulated as a regularized image recovery problem where both the transmitted data and prior knowledge about the properties of the original image are used. This is accomplished by minimizing an objective function, using iterative algorithms, which captures the smoothness properties of the original image. Experimental results are presented which demonstrate that the proposed regularized algorithms yield reconstructed images with superior quality, both visually and using objective distance metrics, to that of traditional decoders that use only the transmitted transform coefficients.

The reconstruction of images from incomplete block discrete cosine transform (BDCT) data is examined. The problem is formulated as one of regularized image recovery. According to this formulation, the image in the decoder is reconstructed by using not only the transmitted data but also prior knowledge about the smoothness of the original image, which complements the transmitted data. Two methods are proposed for solving this regularized recovery problem. The first is based on the theory of projections onto convex sets (POCS) while the second is based on the constrained least squares (CLS) approach. For the POCS-based method, a new constraint set is defined that conveys smoothness information not captured by the transmitted BDCT coefficients, and the projection onto it is computed. For the CLS method an objective function is proposed that captures the smoothness properties of the original image. Iterative algorithms are introduced for its minimization. Experimental results are presented.>