Although deep learning-based algorithms have demonstrated excellent performance in automated emotion recognition via electroencephalogram (EEG) signals, variations across brain signal patterns of individuals can diminish the model’s effectiveness when applied across different subjects. While transfer learning techniques have exhibited promising outcomes, they still encounter challenges related to inadequate feature representations and may overlook the fact that source subjects themselves can possess distinct characteristics. In this work, we propose a multi-source domain adaptation approach with a transformer-based feature generator (MSDA-TF) designed to leverage information from multiple sources. The proposed feature generator retains convolutional layers to capture shallow spatial, temporal, and spectral EEG data representations, while self-attention mechanisms extract global dependencies within these features. During the adaptation process, we group the source subjects based on correlation values and aim to align the moments of the target subject with each source as well as within the sources. MSDA-TF is validated on the SEED dataset and is shown to yield promising results.

Existing physical model-based imaging methods for ultrasound elasticity reconstruction utilize fixed variational regularizers that may not be appropriate for the application of interest or may not capture complex spatial prior information about the underlying tissues. On the other hand, end-to-end learning-based methods count solely on the training data, not taking advantage of the governing physical laws of the imaging system. Integrating learning-based priors with physical forward models for ultrasound elasticity imaging, we present a joint reconstruction framework which guarantees that learning driven reconstructions are consistent with the underlying physics. For solving the elasticity inverse problem as a regularized optimization problem, we propose a plug-and-play (PnP) reconstruction approach in which each iteration of the elasticity image estimation process involves separate updates incorporating data fidelity and learning-based regularization. In this methodology, the data fidelity term is developed using a statistical linear algebraic model of quasi-static equilibrium equation revealing the relationship of the observed displacement fields to the unobserved elastic modulus. The regularizer comprises a convolutional neural network (CNN) based denoiser that captures the learned prior structure of the underlying tissues. Preliminary simulation results demonstrate the robustness and effectiveness of the proposed approach with limited training datasets and noisy displacement measurements.

The key role of emotions in human life is undeniable. The question of whether there exists a brain pattern associated with a specific emotion is the theme of many affective neuroscience studies. In this work, we bring to bear graph signal processing (GSP) techniques to tackle the problem of automatic emotion recognition using brain signals. GSP is an extension of classical signal processing methods to complex networks where there exists an inherent relation graph. With the help of GSP, we propose a new framework for learning class-specific discriminative graphs. To that end, firstly we assume for each class of observations there exists a latent underlying graph representation. Secondly, we consider the observations are smooth on their corresponding class-specific sough graph while they are non-smooth on other classes’ graphs. The learned class-specific graph-based representations can act as sub-dictionaries and be utilized for the task of emotion classification. Applying the proposed method on an electroencephalogram (EEG) emotion recognition dataset indicates the superiority of our framework over other state-of-the-art methods.

Resting-state brain networks represent the intrinsic state of the brain during the majority of cognitive and sensorimotor tasks. However, no study has yet presented concise predictors of task-induced vigilance variability from spectro-spatial features of the resting-state electroencephalograms (EEG). In this study, ten healthy volunteers have participated in fixed-sequence, varying-duration sessions of sustained attention to response task (SART) for over 100 minutes. A novel and adaptive cumulative vigilance scoring (CVS) scheme is proposed based on tonic performance and response time. Multiple linear regression (MLR) using feature relevance analysis has shown that average CVS, average response time, and variabilities of these scores can be predicted (p < 0.05) from the resting-state band-power ratios of EEG signals. Cross-validated neural networks also captured different associations for narrow-band beta and wide-band gamma and differences between the high- and low-attention networks in temporal regions. The proposed framework and these first findings on stable and significant attention predictors from the power ratios of resting-state EEG can be useful in brain-computer interfacing and vigilance monitoring applications.

Stroke-induced disturbances of large-scale cortical networks are known to be associated with the extent of motor deficits. We argue that identifying brain networks representative of motor behavior in the resting brain would provide significant insights for current neurorehabilitation approaches. Particularly, we aim to investigate the global configuration of brain rhythms and their relation to motor skill, instead of learning performance as broadly studied. We empirically approach this problem by conducting a three-dimensional physical space visuomotor learning experiment during electroencephalographic (EEG) data recordings with thirty-seven healthy participants. We demonstrate that across-subjects variations in average movement smoothness as the quantified measure of subjects' motor skills can be predicted from the global configuration of resting-state EEG alpha-rhythms (8-14 Hz) recorded prior to the experiment. Importantly, this neural signature of motor skill was found to be orthogonal to (independent of) task-as well as to learning-related changes in alpha-rhythms, which we interpret as an organizing principle of the brain. We argue that disturbances of such configurations in the brain may contribute to motor deficits in stroke, and that reconfiguring stroke patients' brain rhythms by neurofeedback may enhance post-stroke neurorehabilitation.

Segmenting images of low quality or with missing data is a challenging problem. In such scenarios, exploiting statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Incorporating prior density of shapes into a Bayesian framework leads to the posterior density of segmenting shapes given the observed data. Most segmentation algorithms that exploit shape priors optimize a cost function based on the posterior density and find a point estimate (e.g., using maximum a posteriori estimation). However, especially when the prior shape density is multimodal leading to a multimodal posterior density, a point estimate does not provide a measure of the degree of confidence in that result, neither does it provide a picture of other probable solutions based on the observed data and the shape priors. With a statistical view, addressing these issues would involve the problem of characterizing the posterior distributions of the shapes of the objects to be segmented. An analytic computation of such posterior distributions is intractable; however, characterization is still possible through their samples. In this paper, we propose an efficient pseudo-marginal Markov chain Monte Carlo (MCMC) sampling approach to draw samples from posterior shape distributions for image segmentation. The computation time of the proposed approach is independent from the training set size. Therefore, it scales well for very large data sets. In addition to better characterization of the statistical structure of the problem, such an approach has the potential to address issues with getting stuck at local optima, suffered by existing shape-based segmentation methods. Our approach is able to characterize the posterior probability density in the space of shapes through its samples, and to return multiple solutions, potentially from different modes of a multimodal probability density, which would be encountered, e.g., in segmenting objects from multiple shape classes. We present promising results on a variety of synthetic and real data sets.

The use of appearance and shape priors in image segmentation is known to improve accuracy; however, existing techniques have several drawbacks. For instance, most active shape and appearance models require landmark points and assume unimodal shape and appearance distributions, and the level set representation does not support construction of local priors. In this paper, we present novel appearance and shape models for image segmentation based on a differentiable implicit parametric shape representation called a disjunctive normal shape model (DNSM). The DNSM is formed by the disjunction of polytopes, which themselves are formed by the conjunctions of half-spaces. The DNSM's parametric nature allows the use of powerful local prior statistics, and its implicit nature removes the need to use landmarks and easily handles topological changes. In a Bayesian inference framework, we model arbitrary shape and appearance distributions using nonparametric density estimations, at any local scale. The proposed local shape prior results in accurate segmentation even when very few training shapes are available, because the method generates a rich set of shape variations by locally combining training samples. We demonstrate the performance of the framework by applying it to both 2-D and 3-D data sets with emphasis on biomedical image segmentation applications.

Shape Boltzmann machine (a type of Deep Boltzmann machine) is a powerful tool for shape modelling; however, has some drawbacks in representation of local shape parts. Disjunctive Normal Shape Model (DNSM) is a strong shape model that can effectively represent local parts of objects. In this paper, we propose a new shape model based on Shape Boltzmann Machine and Disjunctive Normal Shape Model which we call Disjunctive Normal Shape Boltzmann Machine (DNSBM). DNSBM learns binary distributions of shapes by taking both local and global shape constraints into account using a type of Deep Boltzmann Machine. The samples generated using DNSBM look realistic. Moreover, DNSBM is capable of generating novel samples that differ from training examples by exploiting the local shape representation capability of DNSM. We demonstrate the performance of DNSBM for shape completion on two different data sets in which exploitation of local shape parts is important for capturing the statistical variability of the underlying shape distributions. Experimental results show that DNSBM is a strong model for representing shapes that are composed of local parts.

Various neuroimaging studies aim to understand the complex nature of human motor behavior. There exists a variety of experimental approaches to study neurophysiological correlates of performance during different motor tasks. As distinct from studies based on visuomotor learning, we investigate changes in electroencephalographic (EEG) activity during an actual physical motor adaptation learning experiment. Based on statistical analysis of EEG signals collected during a force-field adaptation task performed with the dominant hand, we observe a modulation of pre-movement upper alpha (10-12 Hz) and lower beta (13-16 Hz) powers over the contralateral region. This modulation is observed to be stronger in lower beta range and, through a regression analysis, is shown to be related with motor adaptation performance on a subject-specific level.

In many image segmentation problems involving limited and low-quality data, employing statistical prior information about the shapes of the objects to be segmented can significantly improve the segmentation result. However, defining probability densities in the space of shapes is an open and challenging problem, especially if the object to be segmented comes from a shape density involving multiple modes (classes). Existing techniques in the literature estimate the underlying shape distribution by extending Parzen density estimator to the space of shapes. In these methods, the evolving curve may converge to a shape from a wrong mode of the posterior density when the observed intensities provide very little information about the object boundaries. In such scenarios, employing both shape- and class-dependent discriminative feature priors can aid the segmentation process. Such features may involve, e.g., intensity-based, textural, or geometric information about the objects to be segmented. In this paper, we propose a segmentation algorithm that uses nonparametric joint shape and feature priors constructed by Parzen density estimation. We incorporate the learned joint shape and feature prior distribution into a maximum a posteriori estimation framework for segmentation. The resulting optimization problem is solved using active contours. We present experimental results on a variety of synthetic and real data sets from several fields involving multimodal shape densities. Experimental results demonstrate the potential of the proposed method.

Level set methods are widely used for image segmentation because of their convenient shape representation for numerical computations and capability to handle topological changes. However, in spite of the numerous works in the literature, the use of level set methods in image segmentation still has several drawbacks. These shortcomings include formation of irregularities of the signed distance function, sensitivity to initialization, lack of locality, and expensive computational cost, which increases dramatically as the number of objects to be simultaneously segmented grows. In this paper, we propose a novel parametric level set method called disjunctive normal level set (DNLS), and apply it to both two-phase (single object) and multiphase (multiobject) image segmentations. DNLS is a differentiable model formed by the union of polytopes, which themselves are created by intersections of half-spaces. We formulate the segmentation algorithm in a Bayesian framework and use a variational approach to minimize the energy with respect to the parameters of the model. The proposed DNLS can be considered as an open framework that allows the use of different appearance models and shape priors. Compared with the conventional level sets available in the literature, the proposed DNLS has the following major advantages: it requires significantly less computational time and memory, it naturally keeps the level set function regular during the evolution, it is more suitable for multiphase and local region-based image segmentations, and it is less sensitive to noise and initialization. The experimental results show the potential of the proposed method.

Segmenting images of low quality or with missing data is a challenging problem. Integrating statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Most shape-based segmentation algorithms optimize an energy functional and find a point estimate for the object to be segmented. This does not provide a measure of the degree of confidence in that result, neither does it provide a picture of other probable solutions based on the data and the priors. With a statistical view, addressing these issues would involve the problem of characterizing the posterior densities of the shapes of the objects to be segmented. For such characterization, we propose a Markov chain Monte Carlo (MCMC) sampling-based image segmentation algorithm that uses statistical shape priors. In addition to better characterization of the statistical structure of the problem, such an approach would also have the potential to address issues with getting stuck at local optima, suffered by existing shape-based segmentation methods. Our approach is able to characterize the posterior probability density in the space of shapes through its samples, and to return multiple solutions, potentially from different modes of a multimodal probability density, which would be encountered, e.g., in segmenting objects from multiple shape classes. We present promising results on a variety of data sets. We also provide an extension for segmenting shapes of objects with parts that can go through independent shape variations. This extension involves the use of local shape priors on object parts and provides robustness to limitations in shape training data size.

Level set methods are widely used for image segmentation because of their capability to handle topological changes. In this paper, we propose a novel parametric level set method called Disjunctive Normal Level Set (DNLS), and apply it to both two phase (single object) and multiphase (multi-object) image segmentations. The DNLS is formed by union of polytopes which themselves are formed by intersections of half-spaces. The proposed level set framework has the following major advantages compared to other level set methods available in the literature. First, segmentation using DNLS converges much faster. Second, the DNLS level set function remains regular throughout its evolution. Third, the proposed multiphase version of the DNLS is less sensitive to initialization, and its computational cost and memory requirement remains almost constant as the number of objects to be simultaneously segmented grows. The experimental results show the potential of the proposed method.

We present an Augmented Lagrangian Method (ALM) for solving image reconstruction problems with a cost function consisting of multiple regularization functions with a data fidelity constraint. The presented technique is used to solve inverse problems related to image reconstruction, including compressed sensing formulations. Our contributions include an improvement for reducing the number of computations required by an existing ALM method, an approach for obtaining the proximal mapping associated with p-norm based regularizers, and lastly a particular ALM for the constrained image reconstruction problem with a hybrid cost function including a weighted sum of the p-norm and the total variation of the image. We present examples from Synthetic Aperture Radar imaging and Computed Tomography.

In this letter, we investigate the trade-off between the quality of multi-sensor fusion decision and the delay of making that decision in a random access sensor network in a particular setting where the correlation between two sensor observations decreases with the increasing distance between these sensors. We propose a system operation wherein the nodes located in a small neighborhood of a sensor node that has successfully transmitted its decision to the fusion center are deactivated to reduce the contention over the random access channel. We propose a utility function that involves the quality and timeliness of the decision and determine the optimal size of this neighborhood analytically under a Markovian system operation model and numerically by simulating the actual system operation. These experiments demonstrate how our model can be used to set this neighborhood size before data collection to achieve a desired trade-off between decision quality and timeliness.

Statistical characterization of morphological changes of dendritic spines is becoming of crucial interest in the field of neurobiology. Automatic detection and segmentation of dendritic spines promises significant reductions on the time spent by the scientists and reduces the subjectivity concerns. In this paper, we present two approaches for automated detection of dendritic spines in 2-photon laser scanning microscopy (2pLSM) images. The first method combines the idea of dot enhancement filters with information from the dendritic skeleton. The second method learns an SVM classifier by utilizing some pre-labeled SIFT feature descriptors and uses the classifier to detect dendritic spines in new images. For the segmentation of detected spines, we employ a watershed-variational segmentation algorithm. We evaluate the proposed approaches by comparing with manual segmentations of domain experts and the results of a noncommercial software, NeuronIQ. Our methods produce promising detection rate with high segmentation accuracy thus can serve as a useful tool for spine analysis.

We consider the problem of synthetic aperture radar (SAR) image formation, where the underlying scene is to be reconstructed from undersampled observed data. Sparsity-based methods for SAR imaging have employed overcomplete dictionaries to represent the magnitude of the complex-valued field sparsely. Selection of an appropriate dictionary with respect to the features of the particular type of underlying scene plays an important role in these methods. In this paper, we develop a new reconstruction method that is based on learning sparsifying dictionaries and using such learned dictionaries in the reconstruction process. Adaptive dictionaries learned from data have the potential to represent the magnitude of complex-valued field more effectively and hence have the potential to widen the applicability of sparsity-based radar imaging. We demonstrate the performance of the proposed method on both synthetic and real SAR images.

In this paper, a sparsity-driven approach is presented for multi-camera tracking in visual sensor networks (VSNs). VSNs consist of image sensors, embedded processors and wireless transceivers which are powered by batteries. Since the energy and bandwidth resources are limited, setting up a tracking system in VSNs is a challenging problem. Motivated by the goal of tracking in a bandwidth-constrained environment, we present a sparsity-driven method to compress the features extracted by the camera nodes, which are then transmitted across the network for distributed inference. We have designed special overcomplete dictionaries that match the structure of the features, leading to very parsimonious yet accurate representations. We have tested our method in indoor and outdoor people tracking scenarios. Our experimental results demonstrate how our approach leads to communication savings without significant loss in tracking performance.

Brain computer interface (BCI) research deals with the problem of establishing direct communication pathways between the brain and external devices. The primary motivation is to enable patients with limited or no muscular control to use external devices by automatically interpreting their intent based on brain electrical activity, measured by, e.g., electroencephalography (EEG). A widely studied BCI set up involves having subjects type letters based on so-called P300 signals generated by their brains in response to visual stimuli. Due to the low signal-to-noise ratio (SNR) of EEG signals, brain signals generated for a single letter often have to be recorded many times to obtain acceptable accuracy, which reduces the typing speed of the system. Conventionally the measured signals for each letter are processed and classified separately. However, in the context of typing letters within words in a particular language, neighboring letters would provide information about the current letter as well. Based on this observation, we propose an approach for incorporation of such information into a BCI-based speller through hidden Markov models (HMM) trained by a language model. We then describe filtering and smoothing algorithms for inference over such a model. Experiments on real EEG data collected in our laboratory demonstrate that incorporation of the language model in this manner results in significant improvements in classification accuracy and bit rate.

Nonquadratic regularization-based image formation is a recently proposed framework for feature-enhanced radar imaging. Specific image formation techniques in this framework have so far focused on enhancing one type of feature, such as strong point scatterers, or smooth regions. However, many scenes contain a number of such feature types. We develop an image formation technique that simultaneously enhances multiple types of features by posing the problem as one of sparse representation based on combined dictionaries. This method is developed based on the sparse representation of the magnitude of the scattered complex-valued field, composed of appropriate dictionaries associated with different types of features. The multiple feature-enhanced reconstructed image is then obtained through a joint optimization problem over the combined representation of the magnitude and the phase of the underlying field reflectivities.

In this letter, we study the impact of compressed data collections from a synthetic aperture radar (SAR) sensor on the reconstruction quality of a scene of interest. Different monostatic and multistatic SAR measurement configurations produce different Fourier sampling patterns. These patterns reflect different spectral and spatial diversity tradeoffs that must be made during task planning. Compressed sensing theory argues that the mutual coherence of the measurement probes is related to the reconstruction performance of sparse domains. With this motivation, we propose a closely related t%-average mutual coherence parameter as a sensing configuration quality parameter and examine its relationship to the reconstruction behavior of various monostatic and ultranarrow-band multistatic configurations. We investigate how this easily computed metric is related to SAR reconstruction quality.

Image formation algorithms in a variety of applications have explicit or implicit dependence on a mathematical model of the observation process. Inaccuracies in the observation model may cause various degradations and artifacts in the reconstructed images. The application of interest in this paper is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data, which cause defocusing of the reconstructed images. Particularly focusing on imaging of fields that admit a sparse representation, we propose a sparsity-driven method for joint SAR imaging and phase error correction. Phase error correction is performed during the image formation process. The problem is set up as an optimization problem in a nonquadratic regularization-based framework. The method involves an iterative algorithm, where each iteration of which consists of consecutive steps of image formation and model error correction. Experimental results show the effectiveness of the approach for various types of phase errors, as well as the improvements that it provides over existing techniques for model error compensation in SAR.

In synthetic aperture radar (SAR) imaging, the presence of moving targets in the scene causes phase errors in the SAR data and subsequently defocusing in the formed image. The defocusing caused by the moving targets exhibits space-variant characteristics, i.e., the defocusing arises only in the parts of the image containing the moving targets, whereas the stationary background is not defocused. Considering that the reflectivity field to be imaged usually admits sparse representation, we propose a sparsity-driven method for joint SAR imaging and removing the defocus caused by moving targets. The method is performed in a nonquadratic regularization based framework by solving an optimization problem, in which prior information about both the scene and phase errors are incorporated as constraints.

Solution of inverse problems in imaging requires the use of a mathematical model of the observation process. However such models often involve errors and uncertainties themselves. The application of interest in this paper is synthetic aperture radar (SAR) imaging, which particularly suffers from motion-induced model errors. These types of errors result in phase errors in SAR data which cause defocusing of the reconstructed image. Mostly, phase errors vary only in cross-range direction. However, in many situations, it is possible to encounter 2D phase errors, which are both range and cross-range dependent. We propose a sparsity-driven method for joint SAR imaging and correction of 1D as well as 2D phase errors. This method performs phase error correction during the image formation process and provides focused, high-resolution images. Experimental results show the effectiveness of the approach.

We present a new end-to-end brain-computer interface system based on electroencephalography (EEG). Our system exploits the P300 signal in the brain, a positive deflection in event-related potentials, caused by rare events. P300 can be used for various tasks, perhaps the most well-known being a spelling device. We have designed a flexible visual stimulus mechanism that can be adapted to user preferences and developed and implemented EEG signal processing, learning and classification algorithms. Our classifier is based on Bayes linear discriminant analysis, in which we have explored various choices and improvements. We have designed data collection experiments for offline and online decision-making and have proposed modifications in the stimulus and decision-making procedure to increase online efficiency. We have evaluated the performance of our system on 8 healthy subjects on a spelling task and have observed that our system achieves higher average speed than state-of-the-art systems reported in the literature for a given classification accuracy.

We propose an approach based on Hidden Markov models (HMMs) combined with principal component analysis (PCA) for classification of four-class single trial motor imagery EEG data for brain computer interfacing (BCI) purposes. We extract autoregressive (AR) parameters from EEG data and use PCA to decrease the number of features for better training of HMMs. We present experimental results demonstrating the improvements provided by our approach over an existing HMM-based EEG single trial classification approach as well as over state-of-the-art classification methods.

Segmentation of brain structures from MR images is crucial in understanding the disease progress, diagnosis, and treatment monitoring. Atlases, showing the expected locations of the structures, are commonly used to start and guide the segmentation process. In many cases, the quality of the atlas may have a significant effect in the final result. In the literature, commonly used atlases may be obtained from one subject's data, only from the healthy, or depict only certain structures that limit their accuracy. Anatomical variations, pathologies, imaging artifacts all could aggravate the problems related to application of atlases. In this paper, we propose to use multiple atlases that are sufficiently different from each other as much as possible to handle such problems. To this effect, we have built a library of atlases and computed their similarity values to each other. Our study showed that the existing atlases have varying levels of similarity for different structures.

It is important for drowsiness detection systems to identify different levels of drowsiness and respond appropriately at each level. This study explores how to discriminate moderate from acute drowsiness by applying computer vision techniques to the human face. In our previous study, spontaneous facial expressions measured through computer vision techniques were used as an indicator to discriminate alert from acutely drowsy episodes. In this study we are exploring which facial muscle movements are predictive of moderate and acute drowsiness. The effect of temporal dynamics of action units on prediction performances is explored by capturing temporal dynamics using an over complete representation of temporal Gabor Filters. In the final system we perform feature selection to build a classifier that can discriminate moderate drowsy from acute drowsy episodes. The system achieves a classification rate of .96 A' in discriminating moderately drowsy versus acutely drowsy episodes. Moreover the study reveals new information in facial behavior occurring during different stages of drowsiness.

Remote sensing with radar is typically an ill-posed linear inverse problem: a scene is to be inferred from limited measurements of scattered electric fields. Parsimonious models provide a compressed representation of the unknown scene and offer a means for regularizing the inversion task. The emerging field of compressed sensing combines nonlinear reconstruction algorithms and pseudorandom linear measurements to provide reconstruction guarantees for sparse solutions to linear inverse problems. This paper surveys the use of sparse reconstruction algorithms and randomized measurement strategies in radar processing. Although the two themes have a long history in radar literature, the accessible framework provided by compressed sensing illuminates the impact of joining these themes. Potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as nonparametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although this paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object.

We propose an image formation algorithm for ultrasound imaging based on sparsity-driven regularization functionals. We consider data collected by synthetic transducer arrays, with the primary motivating application being nondestructive evaluation. Our framework involves the use of a physical optics-based forward model of the observation process; the formulation of an optimization problem for image formation; and the solution of that problem through efficient numerical algorithms. Our sparsity-driven, model-based approach achieves the preservation of physical features while suppressing spurious artifacts. It also provides robust reconstructions in the case of sparse observation apertures. We demonstrate the effectiveness of our imaging strategy on real ultrasound data

Some applications in remote sensing require estimating a field containing a discontinuity whose exact location is a priori unknown. Such fields of interest include sea surface temperature in oceanography and soil moisture in hydrology. For the former, oceanic fronts form a temperature discontinuity, while in the latter sharp changes exist across the interface between soil types. To complicate the estimation process, remotely sensed measurements often exhibit regions of missing observations due to occlusions such as cloud cover. Similarly, water surface and ground-based sensors usually provide only an incomplete set of measurements. Traditional methods of interpolation and smoothing for estimating the fields from such potentially sparse measurements often blur across the discontinuities in the field.

We propose two methods for the estimation of sparse communication channels. In the first method, we consider the problem of channel estimation based on training symbols, and formulate it as an optimization problem. In this formulation, we combine the objective of fidelity to the received data with a non-quadratic constraint reflecting the prior information about the sparsity of the channel. This approach leads to accurate channel estimates with much shorter training sequences than conventional methods. The second method we propose is aimed at taking advantage of any available training-based data, as well as any "blind" data based on unknown, constant modulus symbols. We propose a semi-blind optimization framework making use of these two types of data, and enforcing the sparsity of the channel, as well as the constant modulus property of the symbols. This approach improves upon the channel estimates based only on training sequences, and also produces accurate estimates for the unknown symbols.

We explore the application of a homotopy continuation-based method for sparse signal representation in overcomplete dictionaries. Our problem setup is based on the basis pursuit framework, which involves a convex optimization problem consisting of terms enforcing data fidelity and sparsity, balanced by a regularization parameter. Choosing a good regularization parameter in this framework is a challenging task. We describe a homotopy continuation-based algorithm to find and trace efficiently all solutions of basis pursuit as a function of the regularization parameter. In addition to providing an attractive alternative to existing optimization methods for solving the basis pursuit problem, this algorithm can also be used to provide an automatic choice for the regularization parameter, based on prior information about the desired number of non-zero components in the sparse representation. Our numerical examples demonstrate the effectiveness of this algorithm in accurately and efficiently generating entire solution paths for basis pursuit, as well as producing reasonable regularization parameter choices. Furthermore, exploring the resulting solution paths in various operating conditions reveals insights about the nature of basis pursuit solutions.

In this paper, we present a new information-theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques. We use level-set methods to implement the resulting evolution. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems. Futhermore, our method, which does not require any training, performs as good as methods based on training.

We consider the problem of enforcing a sparsity prior in underdetermined linear problems, which is also known as sparse signal representation in overcomplete bases. The problem is combinatorial in nature, and a direct approach is computationally intractable, even for moderate data sizes. A number of approximations have been considered in the literature, including stepwise regression, matching pursuit and its variants, and, recently, basis pursuit (/spl lscr//sub 1/) and also /spl lscr//sub p/-norm relaxations with p<1. Although the exact notion of sparsity (expressed by an /spl lscr//sub 0/-norm) is replaced by /spl lscr//sub 1/ and /spl lscr//sub p/ norms in the latter two, it can be shown that under some conditions these relaxations solve the original problem exactly. The seminal paper of D.L. Donoho and X. Huo (see Stanford Univ. Tech. report: http://www-sccm.stanford.edu/pub/sccm/sccm02-17.pdf) establishes this fact for /spl lscr//sub 1/ (basis pursuit) for a special case where the linear operator is composed of an orthogonal pair. We extend their results to a general underdetermined linear operator. Furthermore, we derive conditions for the equivalence of /spl lscr//sub 0/ and /spl lscr//sub p/ problems, and extend the results to the problem of enforcing sparsity with respect to a transformation (which includes total variation priors as a special case). Finally, we describe an interesting result relating the sign patterns of solutions to the question of /spl lscr//sub 1/-/spl lscr//sub 0/ equivalence.

An information-theoretic method for multiphase image segmentation, in an active contour-based framework is proposed. Our approach is based on nonparametric density estimates, and is able to solve problems involving arbitrary probability densities for the region intensities. This is achieved by maximizing the mutual information between the region labels and the image pixel intensities, in order to segment up to 2/sup m/ regions using m curves. The method does not require any prior training regarding the regions of interest, but rather learns the probability densities during the evolution process. We present some illustrative experimental results, demonstrating the power of the proposed segmentation approach.

We propose a novel non-parametric technique for source localization with passive sensor arrays. Our approach involves formulation of the problem in a variational framework where regularizing sparsity constraints are incorporated to achieve super-resolution and noise suppression. Compared to various source localization schemes, our approach offers increased resolution, significantly reduced sidelobes, and improved robustness to limitations in data quality and quantity. We demonstrate the effectiveness of the method on simulated data.

We propose a method for edge-preserving regularized reconstruction in coherent imaging systems. In our framework, image formation from measured data is achieved through the minimization of a cost function, which includes nonquadratic regularizing constraints for suppressing noise artifacts, while preserving the object boundaries in the reconstruction. The cost function we use effectively deals with the complex-valued and random-phase nature of the scattered field, which is inherent in many coherent systems. We solve the challenging optimization problems posed in our framework by a novel extension of half-quadratic regularization methods. We present experimental results from three coherent imaging applications: digital holography, synthetic aperture radar, and medical ultrasound. The proposed technique produces images where coherent speckle artifacts are effectively suppressed, and boundaries between different regions in the scene are preserved.

We present a novel information theoretic approach to image segmentation. We cast the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries. We assume that the probability densities associated with the image pixel intensities within each region are completely unknown a priori, and we formulate the problem based on nonparametric density estimates. Due to the nonparametric structure, our method does not require the image regions to have a particular type of probability distribution, and does not require the extraction and use of a particular statistic. We solve the information-theoretic optimization problem by deriving the associated gradient flows and applying curve evolution techniques. We use fast level set methods to implement the resulting evolution The evolution equations are based on nonparametric statistics, and have an intuitive appeal. The experimental results based on both synthetic and real images demonstrate that the proposed technique can solve a variety of challenging image segmentation problems.

In this paper, we introduce a novel approach for simultaneous restoration and segmentation of blurred noisy images by approaching a variant of the Mumford-Shah functional from a curve evolution perspective. In particular, by viewing the active contour as the set of discontinuities in the image, we derive a gradient flow to minimize an extended Mumford-Shah functional where the known blurring function is incorporated as part of the data fidelity term. Each gradient step involves solving a discrete approximation of the corresponding partial differential equation to obtain a smooth and deblurred estimate of the observed image without blurring across the curve. The experimental results based on both synthetic and real images demonstrate that the proposed method segments and restores the blurred images effectively. We conclude that our work is an edge-preserving image restoration technique that couples segmentation, denoising, and deblurring within a single framework. In addition, this framework provides an intellectual connection between regularization theory (used to solve the deblurring inverse problem) and the theory of curve evolution.

We develop a method for the formation of spotlight-mode synthetic aperture radar (SAR) images with enhanced features. The approach is based on a regularized reconstruction of the scattering field which combines a tomographic model of the SAR observation process with prior information regarding the nature of the features of interest. Compared to conventional SAR techniques, the method we propose produces images with increased resolution, reduced sidelobes, reduced speckle and easier-to-segment regions. Our technique effectively deals with the complex-valued, random-phase nature of the underlying SAR reflectivities. An efficient and robust numerical solution is achieved through extensions of half-quadratic regularization methods to the complex-valued SAR problem. We demonstrate the performance of the method on synthetic and real SAR scenes.

We propose an enhanced image reconstruction method for spotlight-mode synthetic aperture radar (SAR). Our approach involves extension of feature preserving regularization techniques developed in other applications to the complex-valued SAR imaging problem. Compared to conventional image formation schemes, our approach offers increased resolvability of point-scatterers, enhancement of object shapes, reduced sidelobes and reduced speckle. We present the effectiveness of the proposed method on synthetic and real SAR scenes.

We propose a regularization-based method for the complex-valued synthetic aperture radar (SAR) image formation problem. The method can produce images with higher resolution than that supported by the measured data, as well as images with reduced variability of reflectivity magnitudes within homogeneous regions and preserved region boundaries. This is achieved by the inclusion of prior information in the regularized data inversion process through nonquadratic potential functions. For this task, we demonstrate the use of a variety of potential functions in our framework. The technique effectively deals with the random-phase nature of the underlying SAR reflectivities. For an efficient numerical solution, we extend half-quadratic regularization methods to this complex-valued problem. We demonstrate the performance of the method on real SAR data.

This study introduces a criteria-based methodology for grasp synthesis. The method allows the use of multiple performance criteria both at the finger and the hand levels, which are used to generate a preliminary grasp and an optimum grasp, respectively. The approach offers reduced complexity by decomposing grasp synthesis into manageable phases. A case study using a physical hand demonstrates the effectiveness of the method.

We propose a method for discrimination of underlying textural structures from spotlight-mode synthetic aperture radar (SAR) returns by using a tomographic data acquisition model as the basis for statistical reasoning. We model the hypothesized textures by statistically self-similar processes and formulate the problem in a hypothesis testing framework in the SAR range profile domain without any image formation. We achieve a near-optimal, computationally efficient evaluation of the likelihood test by transforming the data into the multiscale domain.

We formulate the spotlight-mode synthetic aperture radar (SAR) imaging problem as a maximum a posteriori (MAP) estimation problem. Our statistical perspective offers an alternative to standard SAR processing techniques by incorporating prior knowledge about either the data quality or the underlying reflectivity function. In our formulation we consider exploiting the similarity between computer assisted tomography (CAT) and spotlight-mode SAR, which was first exposed by Munson et al. (1983). We present the effectiveness of the proposed approach by imagery formed from simulated spotlight-mode SAR data.