Recent advances in Neural Architecture Search (NAS) are essentially attributed to Performance Estimation (PE), i.e., a method aims to effectively estimate an architecture. Meanwhile, Kendall's $\tau$τ is well recognized as the principled evaluation criteria for PE strategies in the literature. We argue that Kendall's $\tau$τ is not the optimal solution. Through extensive experiments and theoretical analysis, we take the initiative to reveal the problem behind the Kendall's $\tau$τ and propose a novel criterion named Minimum Keeping Ratio (MKR), which is closely connected to the final performance of NAS. It allows us to compare different PE approaches in a unified perspective, and use effective ablation studies to verify common beliefs and key differences of PE strategies. Based on the findings from MKR, we are able to derive a simple NAS method by integrating different PE strategies with random sampling. Such a method shows very strong performance in efficiency and effectiveness through extensive experiments on different challenging benchmarks. In particular, our simple random sampling NAS finds the optimal architecture in NASbenchMacro, NASbench201, and NASbench301. It is also well generalized to different search spaces (MobileNet) and tasks (semantic segmentation), finding an architecture surpasses the previous state-of-the-art architectures by 4.25 mIoU under $ 600M$600M FLOPs on ADE20K. Codes are available at https://anonymous.4open.science/r/Anonymization11264.

Choroidal neovascularization (CNV), a primary characteristic of wet age-related macular degeneration (wet AMD), represents a leading cause of blindness worldwide. In clinical practice, optical coherence tomography angiography (OCTA) is commonly used for studying CNV-related pathological changes, due to its micron-level resolution and non-invasive nature. Thus, accurate segmentation of CNV regions and vessels in OCTA images is crucial for clinical assessment of wet AMD. However, challenges existed due to irregular CNV shapes and imaging limitations like projection artifacts, noises and boundary blurring. Moreover, the lack of publicly available datasets constraints the CNV analysis. To address these challenges, this paper constructs the first publicly accessible CNV dataset (CNVSeg), and proposes a novel multilateral graph convolutional interaction-enhanced CNV segmentation network (MTG-Net). This network integrates both region and vessel morphological information, exploring semantic and geometric duality constraints within the graph domain. Specifically, MTG-Net consists of a multi-task framework and two graph-based cross-task modules: Multilateral Interaction Graph Reasoning (MIGR) and Multilateral Reinforcement Graph Reasoning (MRGR). The multi-task framework encodes rich geometric features of lesion shapes and surfaces, decoupling the image into three task-specific feature maps. MIGR and MRGR iteratively reason about higher-order relationships across tasks through a graph mechanism, enabling complementary optimization for task-specific objectives. Additionally, an uncertainty-weighted loss is proposed to mitigate the impact of artifacts and noise on segmentation accuracy. Experimental results demonstrate that MTG-Net outperforms existing methods, achieving a Dice socre of 87.21% for region segmentation and 88.12% for vessel segmentation.

Brain tissue and tumor extraction plays a pivotal role in medical care and clinical research. Leveraging the diverse and complementary information provided by different imaging modalities is crucial to the success of these applications. However, existing deep learning-based methods exhibit limitations in two major aspects. First, they ignore the incorporation of task-oriented regularization when fusing multi-modal features, leading to suboptimal latent space learning. Second, these methods tend to overlook the explicit modeling and exploitation of prediction uncertainty, despite the strong correlation between prediction uncertainty and errors. To address these issues, we propose a novel lightweight network with uncertainty-guided latent space refinement for multi-modal brain tissue and tumor extraction, called UMNet. Particularly, UMNet features a modality-specific uncertainty-regularized feature fusion module (M-SUM), which facilitates latent space refinement to enable a more informed and effective aggregation of complementary multi-modal information. Additionally, we design an uncertainty-enhanced loss function (U-Loss) to explicitly harness the connection between prediction uncertainty and errors. Experimental results demonstrate that our proposed UMNet achieves promising performance, outperforming state-of-the-art methods for both brain tissue and tumor extraction tasks.

Accurate segmentation of blood vessels is essential for various clinical assessments and postoperative analyses. However, the inherent challenges of vascular imaging-such as sparsity, fine granularity, low contrast, data distribution variability, and the critical need for preserving topological integrity-make generalized vessel segmentation particularly complex. While specialized segmentation methods have been developed for specific anatomical regions, their over-reliance on tailored models hinders broader applicability and generalization. General-purpose segmentation models introduced in medical imaging often fail to address critical vascular characteristics, including the connectivity of segmentation results. In this study, we propose OVS-Net, an optimized vessel segmentation framework designed to generalize across diverse vessel structures and imaging modalities. It introduces a dual-branch architecture design for improving small vessel segmentation and a morphology-aware correction module to preserve vascular topology and connectivity. We compiled a comprehensive multi-modality dataset from 17 datasets to train and benchmark the proposed OVS-Net against 6 SAM-based methods and 17 expert models under various conditions. The results demonstrate that our approach achieves superior segmentation accuracy, generalization, and a 34.6% improvement in connectivity, underscoring its potential for clinical applications. The code and dataset information are available at https://github.com/Hk416mod2/OVS-Net.

Vision foundation models have shown great potential in improving generalizability and data efficiency, especially for medical image segmentation since medical image datasets are relatively small due to high annotation costs and privacy concerns. However, current research on foundation models predominantly relies on transformers. The high quadratic complexity and large parameter counts make these models computationally expensive, limiting their potential for clinical applications. In this work, we introduce Swin-UMamba†, a novel Mamba-based model for medical image segmentation that seamlessly leverages the power of the vision foundation model, which is also computationally efficient with the linear complexity of Mamba. Moreover, we investigated and verified the impact of the vision foundation model on medical image segmentation, in which a self-supervised model adaptation scheme was designed to bridge the gap between natural and medical data. Notably, Swin-UMamba† outperforms 7 state-of-the-art methods, including CNN-based, transformer-based, and Mamba-based approaches across AbdomenMRI, Encoscopy, and Microscopy datasets. The code and models are publicly available at: https://github.com/JiarunLiu/Swin-UMamba.

Heterogeneous data captured by different scanning devices and imaging protocols can affect the generalization performance of the deep learning magnetic resonance (MR) reconstruction model. While a centralized training model is effective in mitigating this problem, it raises concerns about privacy protection. Federated learning is a distributed training paradigm that can utilize multi-institutional data for collaborative training without sharing data. However, existing federated learning MR image reconstruction methods rely on models designed manually by experts, which are complex and computationally expensive, suffering from performance degradation when facing heterogeneous data distributions. In addition, these methods give inadequate consideration to fairness issues, namely ensuring that the model's training does not introduce bias towards any specific dataset's distribution. To this end, this paper proposes a generalizable federated neural architecture search framework for accelerating MR imaging (GAutoMRI). Specifically, automatic neural architecture search is investigated for effective and efficient neural network representation learning of MR images from different centers. Furthermore, we design a fairness adjustment approach that can enable the model to learn features fairly from inconsistent distributions of different devices and centers, and thus facilitate the model to generalize well to the unseen center. Extensive experiments show that our proposed GAutoMRI has better performances and generalization ability compared with seven state-of-the-art federated learning methods. Moreover, the GAutoMRI model is significantly more lightweight, making it an efficient choice for MR image reconstruction tasks. The code will be made available at https://github.com/ternencewu123/GAutoMRI.

Federated cross learning has shown impressive performance in medical image segmentation. However, it encounters the catastrophic forgetting issue caused by data heterogeneity across different clients and is particularly pronounced when simultaneously facing pixelwise label deficiency problem. In this article, we propose a novel federated cross-incremental self-supervised learning method, coined FedCSL, which not only can enable any client in the federation incrementally yet effectively learn from others without inducing knowledge forgetting or requiring massive labeled samples, but also preserve maximum data privacy. Specifically, to overcome the catastrophic forgetting issue, a novel cross-incremental collaborative distillation (CCD) mechanism is proposed, which distills explicit knowledge learned from previous clients to subsequent clients based on secure multiparty computation (MPC). Besides, an effective retrospect mechanism is designed to rearrange the training sequence of clients per round, further releasing the power of CCD by enforcing interclient knowledge propagation. In addition, to alleviate the need of large-scale densely annotated pretraining medical datasets, we also propose a two-stage training framework, in which federated cross-incremental self-supervised pretraining paradigm first extracts robust yet general image-level patterns across multi-institutional data silos via a novel round-robin distributed masked image modeling (MIM) pipeline; then, the resulting visual concepts, e.g., semantics, are transferred to the federated cross-incremental supervised fine-tuning paradigm, favoring various cross-silo medical image segmentation tasks. The experimental results on public datasets demonstrate the effectiveness of the proposed method as well as the consistently superior performance of our method over most state-of-the-art methods quantitatively and qualitatively.

Full quantification of brain PET requires the blood input function (IF), which is traditionally achieved through an invasive and time-consuming arterial catheter procedure, making it unfeasible for clinical routine. This study presents a deep learning based method to estimate the input function (DLIF) for a dynamic brain FDG scan. A long short-term memory combined with a fully connected network was used. The dataset for training was generated from 85 total-body dynamic scans obtained on a uEXPLORER scanner. Time-activity curves from 8 brain regions and the carotid served as the input of the model, and labelled IF was generated from the ascending aorta defined on CT image. We emphasize the goodness-of-fitting of kinetic modeling as an additional physical loss to reduce the bias and the need for large training samples. DLIF was evaluated together with existing methods in terms of RMSE, area under the curve, regional and parametric image quantifications. The results revealed that the proposed model can generate IFs that closer to the reference ones in terms of shape and amplitude compared with the IFs generated using existing methods. All regional kinetic parameters calculated using DLIF agreed with reference values, with the correlation coefficient being 0.961 (0.913) and relative bias being 1.68±8.74% (0.37±4.93%) for [Formula: see text] ( [Formula: see text]. In terms of the visual appearance and quantification, parametric images were also highly identical to the reference images. In conclusion, our experiments indicate that a trained model can infer an image-derived IF from dynamic brain PET data, which enables subsequent reliable kinetic modeling.

Recent advances in 3D point cloud analysis bring a diverse set of network architectures to the field. However, the lack of a unified framework to interpret those networks makes any systematic comparison, contrast, or analysis challenging, and practically limits healthy development of the field. In this paper, we take the initiative to explore and propose a unified framework called PointMeta, to which the popular 3D point cloud analysis approaches could fit. This brings three benefits. First, it allows us to compare different approaches in a fair manner, and use quick experiments to verify any empirical observations or assumptions summarized from the comparison. Second, the big picture brought by PointMeta enables us to think across different components, and revisit common beliefs and key design decisions made by the popular approaches. Third, based on the learnings from the previous two analyses, by doing simple tweaks on the existing approaches, we are able to derive a basic building block, termed PointMetaBase. It shows very strong performance in efficiency and effectiveness through extensive experiments on challenging benchmarks, and thus verifies the necessity and benefits of high-level interpretation, contrast, and comparison like PointMeta. In particular, PointMetaBase surpasses the previous state-of-the-art method by 0.7%/1.4/%2.1% mIoU with only 2%/11%/13% of the computation cost on the S3DIS datasets. The code and models are available at https://github.com/linhaojia13/PointMetaBase.

With the successful application of deep learning to magnetic resonance (MR) imaging, parallel imaging techniques based on neural networks have attracted wide attention. However, in the absence of high-quality, fully sampled datasets for training, the performance of these methods is limited. And the interpretability of models is not strong enough. To tackle this issue, this paper proposes a Physics-bAsed unsupeRvised Contrastive rEpresentation Learning (PARCEL) method to speed up parallel MR imaging. Specifically, PARCEL has a parallel framework to contrastively learn two branches of model-based unrolling networks from augmented undersampled multi-coil k-space data. A sophisticated co-training loss with three essential components has been designed to guide the two networks in capturing the inherent features and representations for MR images. And the final MR image is reconstructed with the trained contrastive networks. PARCEL was evaluated on two vivo datasets and compared to five state-of-the-art methods. The results show that PARCEL is able to learn essential representations for accurate MR reconstruction without relying on fully sampled datasets. The code will be made available at https://github.com/ternencewu123/PARCEL.

As an effective way to integrate the information contained in multiple medical images under different modalities, medical image synthesis and fusion have emerged in various clinical applications such as disease diagnosis and treatment planning. In this paper, an invertible and variable augmented network (iVAN) is proposed for medical image synthesis and fusion. In iVAN, the channel number of the network input and output is the same through variable augmentation technology, and data relevance is enhanced, which is conducive to the generation of characterization information. Meanwhile, the invertible network is used to achieve the bidirectional inference processes. Empowered by the invertible and variable augmentation schemes, iVAN not only be applied to the mappings of multi-input to one-output and multi-input to multi-output, but also to the case of one-input to multi-output. Experimental results demonstrated superior performance and potential task flexibility of the proposed method, compared with existing synthesis and fusion methods.

Federated learning (FL) can be used to improve data privacy and efficiency in magnetic resonance (MR) image reconstruction by enabling multiple institutions to collaborate without needing to aggregate local data. However, the domain shift caused by different MR imaging protocols can substantially degrade the performance of FL models. Recent FL techniques tend to solve this by enhancing the generalization of the global model, but they ignore the domain-specific features, which may contain important information about the device properties and be useful for local reconstruction. In this paper, we propose a specificity-preserving FL algorithm for MR image reconstruction (FedMRI). The core idea is to divide the MR reconstruction model into two parts: a globally shared encoder to obtain a generalized representation at the global level, and a client-specific decoder to preserve the domain-specific properties of each client, which is important for collaborative reconstruction when the clients have unique distribution. Such scheme is then executed in the frequency space and the image space respectively, allowing exploration of generalized representation and client-specific properties simultaneously in different spaces. Moreover, to further boost the convergence of the globally shared encoder when a domain shift is present, a weighted contrastive regularization is introduced to directly correct any deviation between the client and server during optimization. Extensive experiments demonstrate that our FedMRI's reconstructed results are the closest to the ground-truth for multi-institutional data, and that it outperforms state-of-the-art FL methods.

Magnetic resonance imaging serves as an essential tool for clinical diagnosis. However, it suffers from a long acquisition time. The utilization of deep learning, especially the deep generative models, offers aggressive acceleration and better reconstruction in magnetic resonance imaging. Nevertheless, learning the data distribution as prior knowledge and reconstructing the image from limited data remains challenging. In this work, we propose a novel Hankel-k-space generative model (HKGM), which can generate samples from a training set of as little as one k-space. At the prior learning stage, we first construct a large Hankel matrix from k-space data, then extract multiple structured k-space patches from the Hankel matrix to capture the internal distribution among different patches. Extracting patches from a Hankel matrix enables the generative model to be learned from the redundant and low-rank data space. At the iterative reconstruction stage, the desired solution obeys the learned prior knowledge. The intermediate reconstruction solution is updated by taking it as the input of the generative model. The updated result is then alternatively operated by imposing low-rank penalty on its Hankel matrix and data consistency constraint on the measurement data. Experimental results confirmed that the internal statistics of patches within single k-space data carry enough information for learning a powerful generative model and providing state-of-the-art reconstruction.

BACKGROUND: The expression changes of some proteins are associated with cancer progression, and can be used as biomarkers in cancer diagnosis. Automated systems have been frequently applied in the large-scale detection of protein biomarkers and have provided a valuable complement for wet-laboratory experiments. For example, our previous work used an immunohistochemical image-based machine learning classifier of protein subcellular locations to screen biomarker proteins that change locations in colon cancer tissues. The tool could recognize the location of biomarkers but did not consider the effect of protein expression level changes on the screening process. RESULTS: In this study, we built an automated classification model that recognizes protein expression levels in immunohistochemical images, and used the protein expression levels in combination with subcellular locations to screen cancer biomarkers. To minimize the effect of non-informative sections on the immunohistochemical images, we employed the representative image patches as input and applied a Wasserstein distance method to determine the number of patches. For the patches and the whole images, we compared the ability of color features, characteristic curve features, and deep convolutional neural network features to distinguish different levels of protein expression and employed deep learning and conventional classification models. Experimental results showed that the best classifier can achieve an accuracy of 73.72% and an F1-score of 0.6343. In the screening of protein biomarkers, the detection accuracy improved from 63.64 to 95.45% upon the incorporation of the protein expression changes. CONCLUSIONS: Machine learning can distinguish different protein expression levels and speed up their annotation in the future. Combining information on the expression patterns and subcellular locations of protein can improve the accuracy of automatic cancer biomarker screening. This work could be useful in discovering new cancer biomarkers for clinical diagnosis and research.

This article aims to build deep learning-based radiomic methods in differentiating vessel invasion from non-vessel invasion in cervical cancer with multi-parametric MRI data. A set of 1,070 dynamic T1 contrast-enhanced (DCE-T1) and 986 T2 weighted imaging (T2WI) MRI images from 167 early-stage cervical cancer patients (January 2014 - August 2018) were used to train and validate deep learning models. Predictive performances were evaluated using receiver operating characteristic (ROC) curve and confusion matrix analysis, with the DCE-T1 showing more discriminative results than T2WI MRI. By adopting an attention ensemble learning strategy that integrates both MRI sequences, the highest average area was obtained under the ROC curve (AUC) of 0.911 (Sensitivity = 0.881 and Specificity = 0.752). The superior performances in this article, when compared to existing radiomic methods, indicate that a wealth of deep learning-based radiomics could be developed to aid radiologists in preoperatively predicting vessel invasion in cervical cancer patients.

Breast density is widely adopted to reflect the likelihood of early breast cancer development. Existing methods of mammographic density classification either require steps of manual operations or achieve only moderate classification accuracy due to the limited model capacity. In this study, we present a radiomics approach based on dilated and attention-guided residual learning for the task of mammographic density classification. The proposed method was instantiated with two datasets, one clinical dataset and one publicly available dataset, and classification accuracies of 88.7 and 70.0 percent were obtained, respectively. Although the classification accuracy of the public dataset was lower than the clinical dataset, which was very likely related to the dataset size, our proposed model still achieved a better performance than the naive residual networks and several recently published deep learning-based approaches. Furthermore, we designed a multi-stream network architecture specifically targeting at analyzing the multi-view mammograms. Utilizing the clinical dataset, we validated that multi-view inputs were beneficial to the breast density classification task with an increase of at least 2.0 percent in accuracy and the different views lead to different model classification capacities. Our method has a great potential to be further developed and applied in computer-aided diagnosis systems. Our code is available at https://github.com/lich0031/Mammographic_Density_Classification.

Assessing the location and extent of lesions caused by chronic stroke is critical for medical diagnosis, surgical planning, and prognosis. In recent years, with the rapid development of 2D and 3D convolutional neural networks (CNN), the encoder-decoder structure has shown great potential in the field of medical image segmentation. However, the 2D CNN ignores the 3D information of medical images, while the 3D CNN suffers from high computational resource demands. This paper proposes a new architecture called dimension-fusion-UNet (D-UNet), which combines 2D and 3D convolution innovatively in the encoding stage. The proposed architecture achieves a better segmentation performance than 2D networks, while requiring significantly less computation time in comparison to 3D networks. Furthermore, to alleviate the data imbalance issue between positive and negative samples for the network training, we propose a new loss function called Enhance Mixing Loss (EML). This function adds a weighted focal coefficient and combines two traditional loss functions. The proposed method has been tested on the ATLAS dataset and compared to three state-of-the-art methods. The results demonstrate that the proposed method achieves the best quality performance in terms of DSC = 0.5349 ± 0.2763 and precision = 0.6331 ± 0.295).

Multi-contrast magnetic resonance (MR) image registration is useful in the clinic to achieve fast and accurate imaging-based disease diagnosis and treatment planning. Nevertheless, the efficiency and performance of the existing registration algorithms can still be improved. In this paper, we propose a novel unsupervised learning-based framework to achieve accurate and efficient multi-contrast MR image registration. Specifically, an end-to-end coarse-to-fine network architecture consisting of affine and deformable transformations is designed to improve the robustness and achieve end-to-end registration. Furthermore, a dual consistency constraint and a new prior knowledge-based loss function are developed to enhance the registration performances. The proposed method has been evaluated on a clinical dataset containing 555 cases, and encouraging performances have been achieved. Compared to the commonly utilized registration methods, including VoxelMorph, SyN, and LT-Net, the proposed method achieves better registration performance with a Dice score of 0.8397± 0.0756 in identifying stroke lesions. With regards to the registration speed, our method is about 10 times faster than the most competitive method of SyN (Affine) when testing on a CPU. Moreover, we prove that our method can still perform well on more challenging tasks with lacking scanning information data, showing the high robustness for the clinical application.

Deep learning, particularly the generative model, has demonstrated tremendous potential to significantly speed up image reconstruction with reduced measurements recently. Rather than the existing generative models that often optimize the density priors, in this work, by taking advantage of the denoising score matching, homotopic gradients of generative density priors (HGGDP) are exploited for magnetic resonance imaging (MRI) reconstruction. More precisely, to tackle the low-dimensional manifold and low data density region issues in generative density prior, we estimate the target gradients in higher-dimensional space. We train a more powerful noise conditional score network by forming high-dimensional tensor as the network input at the training phase. More artificial noise is also injected in the embedding space. At the reconstruction stage, a homotopy method is employed to pursue the density prior, such as to boost the reconstruction performance. Experiment results implied the remarkable performance of HGGDP in terms of high reconstruction accuracy. Only 10% of the k-space data can still generate image of high quality as effectively as standard MRI reconstructions with the fully sampled data.

This work exploits the basic denoising autoencoding (DAE) as enhanced priori for color image restoration (IR). The proposed method consists of two steps: enhanced DAE network learning and iterative restoration. To be special, at the training phase, a denoising network taking 6-dimensional variable as input is trained. Then, the network-driven high-dimensional prior information embedded DAE priori is utilized in the iterative restoration procedure. We first map the intermediate color image to be 6-dimensional and employ the higher-dimensional network to handle its corrupted version. The average operator is used to turn it back to the 3-channel image. The higher-dimensional prior alleviates the issue of the basic DAE that getting trapped in local optimal solution and effectively overcomes the instability. Experimental results on single image super-restoration (SISR) and deblurring demonstrate that the proposed algorithm can achieve good performance and prime visual inspection.

The integration of compressed sensing and parallel imaging (CS-PI) has shown an increased popularity in recent years to accelerate magnetic resonance (MR) imaging. Among them, calibration-free techniques have presented encouraging performances due to its capability in robustly handling the sensitivity information. Unfortunately, existing calibration-free methods have only explored joint-sparsity with direct analysis transform projections. To further exploit joint-sparsity and improve reconstruction accuracy, this paper proposes to Learn joINt-sparse coDes for caliBration-free parallEl mR imaGing (LINDBERG) by modeling the parallel MR imaging problem as an - - minimization objective with an norm constraining data fidelity, Frobenius norm enforcing sparse representation error and the mixed norm triggering joint sparsity across multichannels. A corresponding algorithm has been developed to alternatively update the sparse representation, sensitivity encoded images and K-space data. Then, the final image is produced as the square root of sum of squares of all channel images. Experimental results on both physical phantom and in vivo data sets show that the proposed method is comparable and even superior to state-of-the-art CS-PI reconstruction approaches. Specifically, LINDBERG has presented strong capability in suppressing noise and artifacts while reconstructing MR images from highly undersampled multichannel measurements.

Most low-rank tensor approximations are NP-hard problems. In this paper, we introduce a novel concept: field-of-experts (FoE) filters guided tensor completion, which aims to integrate the strengths of the emerging tensor completion method and the conventional FoE filters. Specifically, the target image is convolved by FoE filters to produce multiview features as a high-order tensor, which captures complementary information from multiple views. In order to impose the concept, we employ two strategies to model the new tensor, one is called FoE filters guided low-rank tensor completion, and another is called FoE filters guided simultaneous tensor decomposition and completion (FoE-STDC). The resulting objectives are solved efficiently by alternating minimization. Extensive experimental results validate the superior performance and robustness of the proposed methods over their corresponding counterparts in all cases. Particularly, the proposed FoE-STDC is superior to the state-of-the-art tensor completion methods.

Foreground detection is fundamental in surveillance video analysis and meaningful toward object tracking and higher level tasks, such as anomaly detection and activity analysis. Nevertheless, existing methods are still limited in accurately detecting the foreground due to the complex scene settings. To robustly handle the diverse background variations and foreground challenges, this paper proposes a Background REpresentation approach With Dictionary Learning and Historical Pixel Maintenance (BREW-DLHPM). Specifically, a dictionary learning problem is formulated at the frame level to adaptively represent the background signals with the varied structure information captured, while a pixel-level maintenance is exploited to grasp the dynamic nature of historical information under the help of the learned background. The simultaneous utilization of dictionary learning and historical pixel maintenance facilitates the accurate description of the background and thus guides a wise foreground detection decision. The proposed BREW-DLHPM has been evaluated on the prestigious change detection challenge data set against 11 state-of-the-art foreground detection approaches and encouraging performances have been achieved by our method.

Image recovery from undersampled data has always been challenging due to its implicit ill-posed nature but becomes fascinating with the emerging compressed sensing (CS) theory. This paper proposes a novel gradient based dictionary learning method for image recovery, which effectively integrates the popular total variation (TV) and dictionary learning technique into the same framework. Specifically, we first train dictionaries from the horizontal and vertical gradients of the image and then reconstruct the desired image using the sparse representations of both derivatives. The proposed method enables local features in the gradient images to be captured effectively, and can be viewed as an adaptive extension of the TV regularization. The results of various experiments on MR images consistently demonstrate that the proposed algorithm efficiently recovers images and presents advantages over the current leading CS reconstruction approaches.

Dictionary learning based sparse modeling has been increasingly recognized as providing high performance in the restoration of noisy images. Although a number of dictionary learning algorithms have been developed, most of them attack this learning problem in its primal form, with little effort being devoted to exploring the advantage of solving this problem in a dual space. In this paper, a novel Fenchel duality based dictionary learning (FD-DL) algorithm has been proposed for the restoration of noise-corrupted images. With the restricted attention to the additive white Gaussian noise, the sparse image representation is formulated as an 2-1 minimization problem, whose dual formulation is constructed using a generalization of Fenchel’s duality theorem and solved under the augmented Lagrangian framework. The proposed algorithm has been compared with four state-of-the-art algorithms, including the local pixel grouping-principal component analysis, method of optimal directions, K-singular value decomposition, and beta process factor analysis, on grayscale natural images. Our results demonstrate that the FD-DL algorithm can effectively improve the image quality and its noisy image restoration ability is comparable or even superior to the abilities of the other four widely-used algorithms.

In recent years Bregman iterative method (or related augmented Lagrangian method) has shown to be an efficient optimization technique for various inverse problems. In this paper, we propose a two-level Bregman Method with dictionary updating for highly undersampled magnetic resonance (MR) image reconstruction. The outer-level Bregman iterative procedure enforces the sampled k-space data constraints, while the inner-level Bregman method devotes to updating dictionary and sparse representation of small overlapping image patches, emphasizing local structure adaptively. Modified sparse coding stage and simple dictionary updating stage applied in the inner minimization make the whole algorithm converge in a relatively small number of iterations, and enable accurate MR image reconstruction from highly undersampled k-space data. Experimental results on both simulated MR images and real MR data consistently demonstrate that the proposed algorithm can efficiently reconstruct MR images and present advantages over the current state-of-the-art reconstruction approach.