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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. [ABSTRACT FROM AUTHOR]

Modern MRI schemes, which rely on compressed sensing or deep learning algorithms to recover MRI data from undersampled multichannel Fourier measurements, are widely used to reduce the scan time. The image quality of these approaches is heavily dependent on the sampling pattern. In this article, we introduce a continuous strategy to optimize the sampling pattern and the network parameters jointly. We use a multichannel forward model, consisting of a non-uniform Fourier transform with continuously defined sampling locations, to realize the data consistency block within a model-based deep learning image reconstruction scheme. This approach facilitates the joint and continuous optimization of the sampling pattern and the CNN parameters to improve image quality. We observe that the joint optimization of the sampling patterns and the reconstruction module significantly improves the performance of most deep learning reconstruction algorithms. The source code of the proposed joint learning framework is available at https://github.com/hkaggarwal/J-MoDL. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their undersampled Fourier coefficients using infimal convolution regularizations. The image is modeled as the superposition of a piecewise constant component and a piecewise linear component. The Fourier coefficients of each component satisfy an annihilation relation, which results in a structured Toeplitz matrix. We exploit the low-rank property of the matrices to formulate a combined regularized optimization problem. In order to solve the problem efficiently and to avoid the high-memory demand resulting from the large-scale Toeplitz matrices, we introduce a fast and a memory-efficient algorithm based on the half-circulant approximation of the Toeplitz matrix. We demonstrate our algorithm in the context of single and multi-channel MR images recovery. Numerical experiments indicate that the proposed algorithm provides improved recovery performance over the state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

We propose a novel deformation corrected compressed sensing (DC-CS) framework to recover contrast enhanced dynamic magnetic resonance images from undersampled measurements. We introduce a formulation that is capable of handling a wide class of sparsity/compactness priors on the deformation corrected dynamic signal. In this work, we consider example compactness priors such as sparsity in temporal Fourier domain, sparsity in temporal finite difference domain, and nuclear norm penalty to exploit low rank structure. Using variable splitting, we decouple the complex optimization problem to simpler and well understood sub problems; the resulting algorithm alternates between simple steps of shrinkage-based denoising, deformable registration, and a quadratic optimization step. Additionally, we employ efficient continuation strategies to reduce the risk of convergence to local minima. The decoupling enabled by the proposed scheme enables us to apply this scheme to contrast enhanced MRI applications. Through experiments on numerical phantom and in vivo myocardial perfusion MRI datasets, we observe superior image quality of the proposed DC-CS scheme in comparison to the classical k-t FOCUSS with motion estimation/correction scheme, and demonstrate reduced motion artifacts over classical compressed sensing schemes that utilize the compact priors on the original deformation uncorrected signal. [ABSTRACT FROM AUTHOR]