Search

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]

In this article, we provide a detailed review of recent advances in the recovery of continuous-domain multidimensional signals from their few nonuniform (multichannel) measurements using structured low-rank (SLR) matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as an SLR matrix completion problem, which includes performance guarantees. We also review fast algorithms that are comparable in complexity to current compressed sensing (CS) methods, which enable the framework's application to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI. [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]

The articles in this special section focus on computational magnetic resonance imaging (MRI) using compressed sensing applications. Presents recent developments in computational MRI. These developments are pushing the frontier of computational imaging beyond CS. Similar to CS, most of these algorithms rely on image representation in one form or another. However, the common recent thread is the departure from handcrafted image representations to learning-based image representations. These learned representations are seamlessly combined with clever measurement strategies to significantly advance the state of the art in a number of areas. Several exciting applications including significantly improved spatial and temporal resolution, a considerable reduction in scan time, measurement of biophysical parameters directly from highly undersampled data, and direct measurement of very high-dimensional data are reviewed in this special issue of SPM. This issue describes key ideas underlying the computational approaches used in MRI. These approaches range from CS algorithms that rely on fixed transforms or dictionaries, to adaptive or shallow-learning algorithms that adapt the image representation to the data to recent deep-learning methods that learn a highly nonlinear representation from exemplar data. The articles provide insight into the capabilities of the current algorithms, their limitations, and their utility in challenging MRI problems. [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]

We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the nonorthogonal nature of the dictionary basis functions. Since the number of degrees-of-freedom of the BCS model is smaller than that of the low-rank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting \ell1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorize–minimize algorithm, which decouples the original criterion into three simpler subproblems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of K-SVD dictionary learning scheme. The use of the \ell1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the \ell0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis functions that can be reliably estimated is restricted by the available measurements. We also observe that the proposed scheme is more robust to local minima compared to K-SVD method, which relies on greedy sparse coding. Our phase transition experiments demonstrate that the BCS scheme provides much better recovery rates than classical Fourier-based CS schemes, while being only marginally worse than the dictionary aware setting. Since the overhead in additionally estimating the dictionary is low, this method can be very useful in dynamic magnetic resonance imaging applications, where the signal is not sparse in known dictionaries. We demonstrate the utility of the BCS scheme in accelerating contrast enhanced dynamic data. We observe superior reconstruction performance with the BCS scheme in comparison to existing low rank and compressed sensing schemes. [ABSTRACT FROM AUTHOR]