Adaptive dictionary learning in sparse gradient domain for image recovery

Attention incorporated network for sharing low-rank, image and k-space information during MR image reconstruction to achieve single breath-hold cardiac Cine imaging

Cardiac Cine Magnetic Resonance Imaging (MRI) provides an accurate assessment of heart morphology and function in clinical practice. However, MRI requires long acquisition times, with recent deep learning-based methods showing great promise to accelerate imaging and enhance reconstruction quality. Existing networks exhibit some common limitations that constrain further acceleration possibilities, including single-domain learning, reliance on a single regularization term, and equal feature contribution. To address these limitations, we propose to embed information from multiple domains, including low-rank, image, and k-space, in a novel deep learning network for MRI reconstruction, which we denote as A-LIKNet. A-LIKNet adopts a parallel-branch structure, enabling independent learning in the k-space and image domain. Coupled information sharing layers realize the information exchange between domains. Furthermore, we introduce attention mechanisms into the network to assign greater weights to more critical coils or important temporal frames. Training and testing were conducted on an in-house dataset, including 91 cardiovascular patients and 38 healthy subjects scanned with 2D cardiac Cine using retrospective undersampling. Additionally, we evaluated A-LIKNet on the real-time prospectively undersampled data from the OCMR dataset. The results demonstrate that our proposed A-LIKNet outperforms existing methods and provides high-quality reconstructions. The network can effectively reconstruct highly retrospectively undersampled dynamic MR images up to 24× accelerations, indicating its potential for single breath-hold imaging.

Attention-Aware Non-Rigid Image Registration for Accelerated MR Imaging

Accurate motion estimation at high acceleration factors enables rapid motion-compensated reconstruction in Magnetic Resonance Imaging (MRI) without compromising the diagnostic image quality. In this work, we introduce an attention-aware deep learning-based framework that can perform non-rigid pairwise registration for fully sampled and accelerated MRI. We extract local visual representations to build similarity maps between the registered image pairs at multiple resolution levels and additionally leverage long-range contextual information using a transformer-based module to alleviate ambiguities in the presence of artifacts caused by undersampling. We combine local and global dependencies to perform simultaneous coarse and fine motion estimation. The proposed method was evaluated on in-house acquired fully sampled and accelerated data of 101 patients and 62 healthy subjects undergoing cardiac and thoracic MRI. The impact of motion estimation accuracy on the downstream task of motion-compensated reconstruction was analyzed. We demonstrate that our model derives reliable and consistent motion fields across different sampling trajectories (Cartesian and radial) and acceleration factors of up to 16x for cardiac motion and 30x for respiratory motion and achieves superior image quality in motion-compensated reconstruction qualitatively and quantitatively compared to conventional and recent deep learning-based approaches. The code is publicly available at https://github.com/lab-midas/GMARAFT.

Magnetic resonance image reconstruction based on image decomposition constrained by total variation and tight frame

OBJECTIVES

Magnetic resonance imaging (MRI) is a commonly used tool in clinical medicine, but it suffers from the disadvantage of slow imaging speed. To address this, we propose a novel MRI reconstruction algorithm based on image decomposition to realize accurate image reconstruction with undersampled k-space data.

METHODS

In our algorithm, the MR images to be recovered are split into cartoon and texture components utilizing image decomposition theory. Different sparse transform constraints are applied to each component based on their morphological structure characteristics. The total variation transform constraint is used for the smooth cartoon component, while the L0 norm constraint of tight frame redundant transform is used for the oscillatory texture component. Finally, an alternating iterative minimization approach is adopted to complete the reconstruction.

RESULTS

Numerous numerical experiments are conducted on several MR images and the results consistently show that, compared with the existing classical compressed sensing algorithm, our algorithm significantly improves the peak signal-to-noise ratio of the reconstructed images and preserves more image details.

CONCLUSIONS

Our algorithm harnesses the sparse characteristics of different image components to reconstruct MR images accurately with highly undersampled data. It can greatly accelerate MRI speed and be extended to other imaging reconstruction fields.

Dual-domain faster Fourier convolution based network for MR image reconstruction

Deep learning methods for fast MRI have shown promise in reconstructing high-quality images from undersampled multi-coil k-space data, leading to reduced scan duration. However, existing methods encounter challenges related to limited receptive fields in dual-domain (k-space and image domains) reconstruction networks, rigid data consistency operations, and suboptimal refinement structures, which collectively restrict overall reconstruction performance. This study introduces a comprehensive framework that addresses these challenges and enhances MR image reconstruction quality. Firstly, we propose Faster Inverse Fourier Convolution (FasterIFC), a frequency domain convolutional operator that significantly expands the receptive field of k-space domain reconstruction networks. Expanding the information extraction range to the entire frequency spectrum according to the spectral convolution theorem in Fourier theory enables the network to easily utilize richer redundant long-range information from adjacent, symmetrical, and diagonal locations of multi-coil k-space data. Secondly, we introduce a novel softer Data Consistency (softerDC) layer, which achieves an enhanced balance between data consistency and smoothness. This layer facilitates the implementation of diverse data consistency strategies across distinct frequency positions, addressing the inflexibility observed in current methods. Finally, we present the Dual-Domain Faster Fourier Convolution Based Network (D2F2), which features a centrosymmetric dual-domain parallel structure based on FasterIFC. This architecture optimally leverages dual-domain data characteristics while substantially expanding the receptive field in both domains. Coupled with the softerDC layer, D2F2 demonstrates superior performance on the NYU fastMRI dataset at multiple acceleration factors, surpassing state-of-the-art methods in both quantitative and qualitative evaluations.

Image Reconstruction for Accelerated MR Scan With Faster Fourier Convolutional Neural Networks

High quality image reconstruction from undersampled k -space data is key to accelerating MR scanning. Current deep learning methods are limited by the small receptive fields in reconstruction networks, which restrict the exploitation of long-range information, and impede the mitigation of full-image artifacts, particularly in 3D reconstruction tasks. Additionally, the substantial computational demands of 3D reconstruction considerably hinder advancements in related fields. To tackle these challenges, we propose the following: 1) A novel convolution operator named Faster Fourier Convolution (FasterFC), aims at providing an adaptable broad receptive field for spatial domain reconstruction networks with fast computational speed. 2) A split-slice strategy that substantially reduces the computational load of 3D reconstruction, enabling high-resolution, multi-coil, 3D MR image reconstruction while fully utilizing inter-layer and intra-layer information. 3) A single-to-group algorithm that efficiently utilizes scan-specific and data-driven priors to enhance k -space interpolation effects. 4) A multi-stage, multi-coil, 3D fast MRI method, called the faster Fourier convolution based single-to-group network (FAS-Net), comprising a single-to-group k -space interpolation algorithm and a FasterFC-based image domain reconstruction module, significantly minimizes the computational demands of 3D reconstruction through split-slice strategy. Experimental evaluations conducted on the NYU fastMRI and Stanford MRI Data datasets reveal that the FasterFC significantly enhances the quality of both 2D and 3D reconstruction results. Moreover, FAS-Net, characterized as a method that can achieve high-resolution (320, 320, 256), multi-coil, (8 coils), 3D fast MRI, exhibits superior reconstruction performance compared to other state-of-the-art 2D and 3D methods.

Dictionary learning compressed sensing reconstruction: pilot validation of accelerated echo planar J-resolved spectroscopic imaging in prostate cancer

Objectives

This study aimed at developing dictionary learning (DL) based compressed sensing (CS) reconstruction for randomly undersampled five-dimensional (5D) MR Spectroscopic Imaging (3D spatial + 2D spectral) data acquired in prostate cancer patients and healthy controls, and test its feasibility at 8x and 12x undersampling factors.

Materials and methods

Prospectively undersampled 5D echo-planar J-resolved spectroscopic imaging (EP-JRESI) data were acquired in nine prostate cancer (PCa) patients and three healthy males. The 5D EP-JRESI data were reconstructed using DL and compared with gradient sparsity-based Total Variation (TV) and Perona-Malik (PM) methods. A hybrid reconstruction technique, Dictionary Learning-Total Variation (DLTV), was also designed to further improve the quality of reconstructed spectra.

Results

The CS reconstruction of prospectively undersampled (8x and 12x) 5D EP-JRESI data acquired in prostate cancer and healthy subjects were performed using DL, DLTV, TV and PM. It is evident that the hybrid DLTV method can unambiguously resolve 2D J-resolved peaks including myo-inositol, citrate, creatine, spermine and choline.

Conclusion

Improved reconstruction of the accelerated 5D EP-JRESI data was observed using the hybrid DLTV. Accelerated acquisition of in vivo 5D data with as low as 8.33% samples (12x) corresponds to a total scan time of 14 min as opposed to a fully sampled scan that needs a total duration of 2.4 h (TR = 1.2 s, 32 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{x}$$\end{document}kx×16 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{y}$$\end{document}ky×8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{z}$$\end{document}kz, 512 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t}_{2}$$\end{document}t2 and 64 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t}_{1}$$\end{document}t1).

Supplementary Information

The online version contains supplementary material available at 10.1007/s10334-022-01029-z.

Analysis of Urban Visual Memes Based on Dictionary Learning: An Example with Urban Image Data

The coexistence of different cultures is a distinctive feature of human society, and globalization makes the construction of cities gradually tend to be the same, so how to find the unique memes of urban culture in a multicultural environment is very important for the development of a city. Most of the previous analyses of urban style have been based on simple classification tasks to obtain the visual elements of cities, lacking in considering the most essential visual elements of cities as a whole. Therefore, based on the image data of ten representative cities around the world, we extract the visual memes via the dictionary learning method, quantify the symmetric similarities and differences between cities by using the memetic similarity, and interpret the reasons for the similarities and differences between cities by using the memetic similarity and sparse representation. The experimental results show that the visual memes have certain limitations among different cities, i.e., the elements composing the urban style are very similar, and the linear combinations of visual memes vary widely as the reason for the differences in the urban style among cities.

Homotopic Gradients of Generative Density Priors for MR Image Reconstruction

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.

Simultaneous image reconstruction and lesion segmentation in accelerated MRI using multitasking learning

PURPOSE

Magnetic resonance imaging (MRI) serves as an important medical imaging modality for a variety of clinical applications. However, the problem of long imaging time limited its wide usage. In addition, prolonged scan time will cause discomfort to the patient, leading to severe image artifacts. On the other hand, manually lesion segmentation is time consuming. Algorithm-based automatic lesion segmentation is still challenging, especially for accelerated imaging with low quality.

METHODS

In this paper, we proposed a multitask learning-based method to perform image reconstruction and lesion segmentation simultaneously, called "RecSeg". Our hypothesis is that both tasks can benefit from the usage of the proposed combined model. In the experiment, we validated the proposed multitask model on MR k-space data with different acceleration factors (2×, 4×, and 6×). Two connected U-nets were used for the tasks of liver and renal image reconstruction and segmentation. A total of 50 healthy subjects and 100 patients with hepatocellular carcinoma were included for training and testing. For the segmentation part, we use healthy subjects to verify organ segmentation, and hepatocellular carcinoma patients to verify lesion segmentation. The organs and lesions were manually contoured by an experienced radiologist.

RESULTS

Experimental results show that the proposed RecSeg yielded the highest PSNR (RecSeg: 32.39 ± 1.64 vs. KSVD: 29.53 ± 2.74 and single U-net: 31.18 ± 1.68, respectively, p < 0.05) and highest structural similarity index measure (SSIM) (RecSeg: 0.93 ± 0.01 vs. KSVD: 0.88 ± 0.02 and single U-net: 0.90 ± 0.01, respectively, p < 0.05) under 6× acceleration. Moreover, in the task of lesion segmentation, it is proposed that RecSeg produced the highest Dice score (RecSeg: 0.86 ± 0.01 vs. KSVD: 0.82 ± 0.01 and single U-net: 0.84 ± 0.01, respectively, p < 0.05).

CONCLUSIONS

This study focused on the simultaneous reconstruction of medical images and the segmentation of organs and lesions. It is observed that the multitask learning-based method can improve performances of both image reconstruction and lesion segmentation.

Image Denoising Based on Fractional Gradient Vector Flow and Overlapping Group Sparsity as Priors

In this paper, a new regularization term in the form of L1-norm based fractional gradient vector flow (LF-GGVF) is presented for the task of image denoising. A fractional order variational method is formulated, which is then utilized for estimating the proposed LF-GGVF. Overlapping group sparsity along with LF-GGVF is used as priors in image denoising optimization framework. The Riemann-Liouville derivative is used for approximating the fractional order derivatives present in the optimization framework. Its role in the framework helps in boosting the denoising performance. The numerical optimization is performed in an alternating manner using the well-known alternating direction method of multipliers (ADMM) and split Bregman techniques. The resulting system of linear equations is then solved using an efficient numerical scheme. A variety of simulated data that includes test images contaminated by additive white Gaussian noise are used for experimental validation. The results of numerical solutions obtained from experimental work demonstrate that the performance of the proposed approach in terms of noise suppression and edge preservation is better when compared with that of several other methods.

Reference-Driven Undersampled MR Image Reconstruction Using Wavelet Sparsity-Constrained Deep Image Prior

Deep learning has shown potential in significantly improving performance for undersampled magnetic resonance (MR) image reconstruction. However, one challenge for the application of deep learning to clinical scenarios is the requirement of large, high-quality patient-based datasets for network training. In this paper, we propose a novel deep learning-based method for undersampled MR image reconstruction that does not require pre-training procedure and pre-training datasets. The proposed reference-driven method using wavelet sparsity-constrained deep image prior (RWS-DIP) is based on the DIP framework and thereby reduces the dependence on datasets. Moreover, RWS-DIP explores and introduces structure and sparsity priors into network learning to improve the efficiency of learning. By employing a high-resolution reference image as the network input, RWS-DIP incorporates structural information into network. RWS-DIP also uses the wavelet sparsity to further enrich the implicit regularization of traditional DIP by formulating the training of network parameters as a constrained optimization problem, which is solved using the alternating direction method of multipliers (ADMM) algorithm. Experiments on in vivo MR scans have demonstrated that the RWS-DIP method can reconstruct MR images more accurately and preserve features and textures from undersampled k-space measurements.

Compressed sensing MRI using an interpolation-free nonlinear diffusion model

PURPOSE

Constraints in extended neighborhood system demand the use of a large number of interpolations in directionality-guided compressed-sensing nonlinear diffusion MR image reconstruction technique. This limits its practical application in terms of computational complexity. The proposed method aims at multifold improvement in its runtime without compromising the image quality.

THEORY AND METHODS

Conventional approach to extended neighborhood computation requires 108 linear interpolations per pixel for 10 sets of neighborhoods. We propose a neighborhood stretching technique that systematically extends the location of neighboring pixels such that 66% to 100% fewer interpolations are required to compute the gradients along multiple directions. A spatial frequency-based deviation measure is then used to choose the most reliable edges from the set of images generated by diffusion along different directions.

RESULTS

The semi-interpolated and interpolation-free diffusion techniques proposed in this paper are compared with the fully interpolated diffusion-based reconstruction by reconstruing multiple multichannel in vivo datasets, undersampled using different sampling patterns at various sampling rates. Results indicate a two- to fivefold increase in reconstruction speed with a potential to generate 1 to 2 dB improvement in peak SNR measure.

CONCLUSION

The proposed method outperforms the state-of-the-art fully interpolated diffusion model and generates high-quality reconstructions for different sampling patterns and acceleration factors with a two- to fivefold increment in reconstruction speed. This makes it the most suitable candidate for edge-preserving penalties used in the compressed sensing MRI reconstruction methods.

A deep error correction network for compressed sensing MRI

BACKGROUND

CS-MRI (compressed sensing for magnetic resonance imaging) exploits image sparsity properties to reconstruct MRI from very few Fourier k-space measurements. Due to imperfect modelings in the inverse imaging, state-of-the-art CS-MRI methods tend to leave structural reconstruction errors. Compensating such errors in the reconstruction could help further improve the reconstruction quality.

RESULTS

In this work, we propose a DECN (deep error correction network) for CS-MRI. The DECN model consists of three parts, which we refer to as modules: a guide, or template, module, an error correction module, and a data fidelity module. Existing CS-MRI algorithms can serve as the template module for guiding the reconstruction. Using this template as a guide, the error correction module learns a CNN (convolutional neural network) to map the k-space data in a way that adjusts for the reconstruction error of the template image. We propose a deep error correction network. Our experimental results show the proposed DECN CS-MRI reconstruction framework can considerably improve upon existing inversion algorithms by supplementing with an error-correcting CNN.

CONCLUSIONS

In the proposed a deep error correction framework, any off-the-shelf CS-MRI algorithm can be used as template generation. Then a deep neural network is used to compensate reconstruction errors. The promising experimental results validate the effectiveness and utility of the proposed framework.

Reference-Driven Compressed Sensing MR Image Reconstruction Using Deep Convolutional Neural Networks without Pre-Training

Deep learning has proven itself to be able to reduce the scanning time of Magnetic Resonance Imaging (MRI) and to improve the image reconstruction quality since it was introduced into Compressed Sensing MRI (CS-MRI). However, the requirement of using large, high-quality, and patient-based datasets for network training procedures is always a challenge in clinical applications. In this paper, we propose a novel deep learning based compressed sensing MR image reconstruction method that does not require any pre-training procedure or training dataset, thereby largely reducing clinician dependence on patient-based datasets. The proposed method is based on the Deep Image Prior (DIP) framework and uses a high-resolution reference MR image as the input of the convolutional neural network in order to induce the structural prior in the learning procedure. This reference-driven strategy improves the efficiency and effect of network learning. We then add the k-space data correction step to enforce the consistency of the k-space data with the measurements, which further improve the image reconstruction accuracy. Experiments on in vivo MR datasets showed that the proposed method can achieve more accurate reconstruction results from undersampled k-space data.

Deep Magnetic Resonance Image Reconstruction: Inverse Problems Meet Neural Networks

Image reconstruction from undersampled k-space data has been playing an important role in fast MRI. Recently, deep learning has demonstrated tremendous success in various fields and has also shown potential in significantly accelerating MRI reconstruction with fewer measurements. This article provides an overview of the deep learning-based image reconstruction methods for MRI. Two types of deep learning-based approaches are reviewed: those based on unrolled algorithms and those which are not. The main structure of both approaches are explained, respectively. Several signal processing issues for maximizing the potential of deep reconstruction in fast MRI are discussed. The discussion may facilitate further development of the networks and the analysis of performance from a theoretical point of view.

CS-MRI reconstruction based on analysis dictionary learning and manifold structure regularization

Compressed sensing (CS) significantly accelerates magnetic resonance imaging (MRI) by allowing the exact reconstruction of image from highly undersampling k-space data. In this process, the high sparsity obtained by the learned dictionary and exploitation of correlation among patches are essential to the reconstructed image quality. In this paper, by a use of these two aspects, we propose a novel CS-MRI model based on analysis dictionary learning and manifold structure regularization (ADMS). Furthermore, a proper tight frame constraint is used to obtain an effective overcomplete analysis dictionary with a high sparsifying capacity. The constructed manifold structure regularization nonuniformly enforces the correlation of each group formed by similar patches, which is more consistent with the diverse nonlocal similarity in realistic images. The proposed model is efficiently solved by the alternating direction method of multipliers (ADMM), in which the fast algorithm for each sub-problem is separately developed. The experimental results demonstrate that main components in the proposed method contribute to the final reconstruction performance and the effectiveness of the proposed model.

Computational ghost imaging via adaptive deep dictionary learning

Ghost imaging has gone through from quantum to classical pseudothermal to computational field over the last two decades. As a kernel part in computational ghost imaging (CGI), the reconstruction algorithm plays a decisive role in imaging quality and system practicality. In order to introduce more prior knowledge into the reconstruction algorithm, existing research adds image patch prior into CGI and improves the imaging efficiency. In this paper, the total variation minimization algorithm via adaptive deep dictionary learning (TVADDL) is proposed to update an adaptive deep dictionary through the CGI reconstruction process. The proposed algorithm framework is able to capture more precise texture features with a multi-layer architecture dictionary and adapt the learned dictionary by gradient descent on CGI reconstruction loss value. The results of simulation and experiment show that TVADDL can achieve higher peak signal-to-noise ratio than the algorithms without patch prior and the algorithms using the shallow dictionary or non-adaptive deep dictionary.

Directionality guided non linear diffusion compressed sensing MR image reconstruction

PURPOSE

Address the shortcomings of edge-preserving filters to preserve the complex nature of edges, by adapting the direction of diffusion to the local variations in intensity function on a subpixel level, thereby achieving a reconstruction accuracy superior to that of data-driven learning-based approaches.

THEORY AND METHODS

Rate of diffusion for edges is found to vary in accordance with their gradient direction. Therefore, the edge preservation is strongly dependent on the direction in which the gradient is computed. Since the directionality of edges varies at different regions of the image, the proposed technique computes the gradients in all possible angular directions and uses a spatial-frequency-based deviation measure to choose the most reliable edges from the images diffused along different directions.

RESULTS

The proposed method is compared with the state-of-the-art data-driven learning-based techniques of block matching and 3D filtering (BM3D), patch-based nonlocal operator (PANO), and dictionary learning MRI (DLMRI). Best results are obtained when directionality of edges is estimated from a prior optimized k-space and shows an improvement in peak signal-to-noise ratio (PSNR) measures by a factor of 2.36 dB, 1.92 dB, and 1.59 dB over BM3D, PANO, and dictionary learning MRI, respectively.

CONCLUSION

The proposed technique prevents the emphasis of false edges and better captures the structural details by a locally varying directionality-guided diffusion to make the error lower than that of the state-of-the-art reconstruction techniques. In addition, a highly parallelizable form of the proposed model promises a significant gain in the reconstruction speed for practical implementations.

Orthogonal tensor dictionary learning for accelerated dynamic MRI

A direct application of the compressed sensing (CS) theory to dynamic magnetic resonance imaging (MRI) reconstruction needs vectorization or matricization of the dynamic MRI data, which is composed of a stack of 2D images and can be naturally regarded as a tensor. This 1D/2D model may destroy the inherent spatial structure property of the data. An alternative way to exploit the multidimensional structure in dynamic MRI is to employ tensor decomposition for dictionary learning, that is, learning multiple dictionaries along each dimension (mode) and sparsely representing the multidimensional data with respect to the Kronecker product of these dictionaries. In this work, we introduce a novel tensor dictionary learning method under an orthonormal constraint on the elementary matrix of the tensor dictionary for dynamic MRI reconstruction. The proposed algorithm alternates sparse coding, tensor dictionary learning, and updating reconstruction, and each corresponding subproblem is efficiently solved by a closed-form solution. Numerical experiments on phantom and synthetic data show significant improvements in reconstruction accuracy and computational efficiency obtained by the proposed scheme over the existing method that uses the 1D/2D model with overcomplete dictionary learning. Graphical abstract Fig. 1 Comparison between (a) the traditional method and (b) the proposed method based on dictionary learning for dynamic MRI reconstruction.

Positive-contrast susceptibility imaging based on first-order primal-dual optimization

PURPOSE

To achieve faster reconstruction and better imaging quality of positive-contrast MRI based on the susceptibility mapping by incorporating a primal-dual (PD) formulation.

METHODS

The susceptibility-based positive contrast MR technique was applied to estimate arbitrary magnetic susceptibility distributions of the metallic devices using a kernel deconvolution algorithm with a regularized ℓ 1 minimization. The regularized positive-contrast inversion problem and its PD formulation were derived. The visualization of the positive contrast and convergence behavior of the PD algorithm were compared with those of the nonlinear conjugate gradient algorithm, fast iterative soft-thresholding algorithm, and alternating direction method of multipliers. These methods were tested and validated on computer simulations and phantom experiments.

RESULTS

The PD approach could provide a faster reconstruction time compared with other methods. Experimental results showed that the PD algorithm could achieve comparable or even better visualization and accuracy of the metallic interventional devices in positive-contrast imaging with different SNRs and orientations to the B₀ field.

CONCLUSION

A susceptibility-based positive-contrast imaging technique by PD algorithm was proposed. The PD approach has more superior performance than other algorithms in terms of reconstruction time and accuracy for imaging the metallic interventional devices.

Compressed sensing MRI based on image decomposition model and group sparsity

The image representation plays an important role in compressed sensing magnetic resonance imaging (CSMRI). However, how to adaptive sparsely represent images is a challenge for accurately reconstructing magnetic resonance (MR) images from highly undersampled data with noise. In order to further improve the reconstruction quality of the MR image, this paper first proposes tight frame-based group sparsity (TFGS) regularization that can capture the structure information of images appropriately, then TFGS regularization is employed to the image cartoon-texture decomposition model to construct CSMRI algorithm, termed cartoon-texture decomposition CSMRI algorithm (CD-MRI). CD-MRI effectively integrates the total variation and TFGS regularization into the image cartoon-texture decomposition framework, and utilizes the sparse priors of image cartoon and texture components to reconstruct MR images. Virtually, CD-MRI exploits the global sparse representations of image cartoon components by the total variation regularization, and explores group sparse representations of image texture components via the adaptive tight frame learning technique and group sparsity regularization. The alternating iterative method combining with the majorization-minimization algorithm is applied to solve the formulated optimization problem. Finally, simulation experiments demonstrate that the proposed algorithm can achieve high-quality MR image reconstruction from undersampled K-space data, and can remove noise in different sampling schemes. Compared to the previous CSMRI algorithms, the proposed approach can lead to better image reconstruction performance and better robustness to noise.

A Novel Dictionary-Based Image Reconstruction for Photoacoustic Computed Tomography

One of the major concerns in photoacoustic computed tomography (PACT) is obtaining a high-quality image using the minimum number of ultrasound transducers/view angles. This issue is of importance when a cost-effective PACT system is needed. On the other hand, analytical reconstruction algorithms such as back projection (BP) and time reversal, when a limited number of view angles is used, cause artifacts in the reconstructed image. Iterative algorithms provide a higher image quality, compared to BP, due to a model used for image reconstruction. The performance of the model can be further improved using the sparsity concept. In this paper, we propose using a novel sparse dictionary to capture important features of the photoacoustic signal and eliminate the artifacts while few transducers is used. Our dictionary is an optimum combination of Wavelet Transform (WT), Discrete Cosine Transform (DCT), and Total Variation (TV). We utilize two quality assessment metrics including peak signal-to-noise ratio and edge preservation index to quantitatively evaluate the reconstructed images. The results show that the proposed method can generate high-quality images having fewer artifacts and preserved edges, when fewer view angles are used for reconstruction in PACT.

Improved parallel image reconstruction using feature refinement

PURPOSE

The aim of this study was to develop a novel feature refinement MR reconstruction method from highly undersampled multichannel acquisitions for improving the image quality and preserve more detail information.

THEORY AND METHODS

The feature refinement technique, which uses a feature descriptor to pick up useful features from residual image discarded by sparsity constrains, is applied to preserve the details of the image in compressed sensing and parallel imaging in MRI (CS-pMRI). The texture descriptor and structure descriptor recognizing different types of features are required for forming the feature descriptor. Feasibility of the feature refinement was validated using three different multicoil reconstruction methods on in vivo data.

RESULTS

Experimental results show that reconstruction methods with feature refinement improve the quality of reconstructed image and restore the image details more accurately than the original methods, which is also verified by the lower values of the root mean square error and high frequency error norm.

CONCLUSION

A simple and effective way to preserve more useful detailed information in CS-pMRI is proposed. This technique can effectively improve the reconstruction quality and has superior performance in terms of detail preservation compared with the original version without feature refinement. Magn Reson Med 80:211-223, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

MR image reconstruction via guided filter

Magnetic resonance imaging (MRI) reconstruction from the smallest possible set of Fourier samples has been a difficult problem in medical imaging field. In our paper, we present a new approach based on a guided filter for efficient MRI recovery algorithm. The guided filter is an edge-preserving smoothing operator and has better behaviors near edges than the bilateral filter. Our reconstruction method is consist of two steps. First, we propose two cost functions which could be computed efficiently and thus obtain two different images. Second, the guided filter is used with these two obtained images for efficient edge-preserving filtering, and one image is used as the guidance image, the other one is used as a filtered image in the guided filter. In our reconstruction algorithm, we can obtain more details by introducing guided filter. We compare our reconstruction algorithm with some competitive MRI reconstruction techniques in terms of PSNR and visual quality. Simulation results are given to show the performance of our new method.

How to deal with color in super resolution reconstruction of images

Super resolution (SR) reconstruction is a profitable technology to acquire high resolution images from low resolution images without replacing devices. This study was concentrated on searching strategies of dealing with color information in the SR reconstruction process. Based on an algorithm with dictionary learning, different algorithms were designed to test which color coordinate systems could obtain better image reconstruction quality, involving color spaces of RGB, YIQ, YCbCr, HSI, HSV, and CIELAB. Their results were compared via typical numerical measures, and the recommended strategies are to adopt merely L* coordinate in CIELAB space or merely Y coordinate of YIQ system.

Two-Layer Tight Frame Sparsifying Model for Compressed Sensing Magnetic Resonance Imaging

Compressed sensing magnetic resonance imaging (CSMRI) employs image sparsity to reconstruct MR images from incoherently undersampled K-space data. Existing CSMRI approaches have exploited analysis transform, synthesis dictionary, and their variants to trigger image sparsity. Nevertheless, the accuracy, efficiency, or acceleration rate of existing CSMRI methods can still be improved due to either lack of adaptability, high complexity of the training, or insufficient sparsity promotion. To properly balance the three factors, this paper proposes a two-layer tight frame sparsifying (TRIMS) model for CSMRI by sparsifying the image with a product of a fixed tight frame and an adaptively learned tight frame. The two-layer sparsifying and adaptive learning nature of TRIMS has enabled accurate MR reconstruction from highly undersampled data with efficiency. To solve the reconstruction problem, a three-level Bregman numerical algorithm is developed. The proposed approach has been compared to three state-of-the-art methods over scanned physical phantom and in vivo MR datasets and encouraging performances have been achieved.

Image reconstruction from few-view CT data by gradient-domain dictionary learning

BACKGROUND

Decreasing the number of projections is an effective way to reduce the radiation dose exposed to patients in medical computed tomography (CT) imaging. However, incomplete projection data for CT reconstruction will result in artifacts and distortions.

OBJECTIVE

In this paper, a novel dictionary learning algorithm operating in the gradient-domain (Grad-DL) is proposed for few-view CT reconstruction. Specifically, the dictionaries are trained from the horizontal and vertical gradient images, respectively and the desired image is reconstructed subsequently from the sparse representations of both gradients by solving the least-square method.

METHODS

Since the gradient images are sparser than the image itself, the proposed approach could lead to sparser representations than conventional DL methods in the image-domain, and thus a better reconstruction quality is achieved.

RESULTS

To evaluate the proposed Grad-DL algorithm, both qualitative and quantitative studies were employed through computer simulations as well as real data experiments on fan-beam and cone-beam geometry.

CONCLUSIONS

The results show that the proposed algorithm can yield better images than the existing algorithms.

A Dictionary Learning Method with Total Generalized Variation for MRI Reconstruction

Reconstructing images from their noisy and incomplete measurements is always a challenge especially for medical MR image with important details and features. This work proposes a novel dictionary learning model that integrates two sparse regularization methods: the total generalized variation (TGV) approach and adaptive dictionary learning (DL). In the proposed method, the TGV selectively regularizes different image regions at different levels to avoid oil painting artifacts largely. At the same time, the dictionary learning adaptively represents the image features sparsely and effectively recovers details of images. The proposed model is solved by variable splitting technique and the alternating direction method of multiplier. Extensive simulation experimental results demonstrate that the proposed method consistently recovers MR images efficiently and outperforms the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.

Undersampled MR Image Reconstruction with Data-Driven Tight Frame

Undersampled magnetic resonance image reconstruction employing sparsity regularization has fascinated many researchers in recent years under the support of compressed sensing theory. Nevertheless, most existing sparsity-regularized reconstruction methods either lack adaptability to capture the structure information or suffer from high computational load. With the aim of further improving image reconstruction accuracy without introducing too much computation, this paper proposes a data-driven tight frame magnetic image reconstruction (DDTF-MRI) method. By taking advantage of the efficiency and effectiveness of data-driven tight frame, DDTF-MRI trains an adaptive tight frame to sparsify the to-be-reconstructed MR image. Furthermore, a two-level Bregman iteration algorithm has been developed to solve the proposed model. The proposed method has been compared to two state-of-the-art methods on four datasets and encouraging performances have been achieved by DDTF-MRI.

Dictionary learning approach for image deconvolution with variance estimation

In this paper, we propose a new dictionary learning approach for image deconvolution, which effectively integrates the Fourier regularization and dictionary learning technique into the deconvolution framework. Specifically, we propose an iterative algorithm with the decoupling of the deblurring and denoising steps in the restoration process. In the deblurring step, we involve a regularized inversion of the blur in the Fourier domain. Then we remove the colored noise using a dictionary learning method in the denoising step. In the denoising step, we propose an approach to update the estimation of noise variance for dictionary learning. We will show that this approach outperforms several state-of-the-art image deconvolution methods in terms of improvement in signal-to-noise ratio and visual quality.

PANDA-T1ρ: Integrating principal component analysis and dictionary learning for fast T1ρ mapping

PURPOSE

Long scanning time greatly hinders the widespread application of spin-lattice relaxation in rotating frame (T1ρ) in clinics. In this study, a novel method is proposed to reconstruct the T1ρ-weighted images from undersampled k-space data and hence accelerate the acquisition of T1ρ imaging.

METHODS

The proposed approach (PANDA-T1ρ) combined the benefit of PCA and dictionary learning when reconstructing image from undersampled data. Specifically, the PCA transform was first used to sparsify the image series along the parameter direction and then the sparsified images were reconstructed by means of dictionary learning and finally solved the images. A variation of PANDA-T1ρ was also developed for the heavy noise case. Numerical simulation and in vivo experiments were carried out with the accelerating factor from 2 to 4 to verify the performance of PANDA-T1ρ.

RESULTS

The reconstructed T1ρ maps using the PANDA-T1ρ method were found to be comparable to the reference at all verified acceleration factors. Moreover, the variation exhibited better performance than the original version when the k-space data were contaminated by heavy noise.

CONCLUSION

PANDA-T1ρ can significantly reduce the scanning time of T1ρ by integrating PCA and dictionary learning and provides better parameter estimation than the state-of-art methods for a fixed acceleration factor.

Accelerating Dynamic Cardiac MR imaging using structured sparse representation

Compressed sensing (CS) has produced promising results on dynamic cardiac MR imaging by exploiting the sparsity in image series. In this paper, we propose a new method to improve the CS reconstruction for dynamic cardiac MRI based on the theory of structured sparse representation. The proposed method user the PCA subdictionaries for adaptive sparse representation and suppresses the sparse coding noise to obtain good reconstructions. An accelerated iterative shrinkage algorithm is used to solve the optimization problem and achieve a fast convergence rate. Experimental results demonstrate that the proposed method improves the reconstruction quality of dynamic cardiac cine MRI over the state-of-the-art CS method.