We develop a variational model and a faster and robust numerical algorithm for simultaneous sensitivity map estimation and image reconstruction in partially parallel MR imaging with significantly under-sampled data. The proposed model uses a maximum likelihood approach to minimizing the residue of data fitting in the presence of independent Gaussian noise. The usage of maximum likelihood estimation dramatically reduces the sensitivity to the selection of model parameter, and increases the accuracy and robustness of the algorithm. Moreover, variable splitting based on the specific structure of the objective function, and alternating direction method of multipliers (ADMM) are used to accelerate the computation. The preliminary results indicate that the proposed method resulted in fast and robust reconstruction.

This paper presents two fast algorithms for total variation–based image reconstruction in a magnetic resonance imaging technique known as partially parallel imaging (PPI), where the inversion matrix is large and ill-conditioned. These algorithms utilize variable splitting techniques to decouple the original problem into more easily solved subproblems. The first method reduces the image reconstruction problem to an unconstrained minimization problem, which is solved by an alternating proximal minimization algorithm. One phase of the algorithm solves a total variation (TV) denoising problem, and the second phase solves an ill-conditioned linear system. Linear and sublinear convergence results are given, and an implementation based on a primal-dual hybrid gradient (PDHG) scheme for the TV problem and on a Barzilai–Borwein scheme for the linear inversion is proposed. The second algorithm exploits the special structure of the PPI reconstruction problem by decomposing it into one subproblem involving Fourier transforms and another subproblem that can be treated by the PDHG scheme. Numerical results and comparisons with recently developed methods indicate the efficiency of the proposed algorithms.

In this paper, we present a fast numerical algorithm for solving total variation and l(1) (TVL1) based image reconstruction with application in partially parallel magnetic resonance imaging. Our algorithm uses variable splitting method to reduce computational cost. Moreover, the Barzilai-Borwein step size selection method is adopted in our algorithm for much faster convergence. Experimental results on clinical partially parallel imaging data demonstrate that the proposed algorithm requires much fewer iterations and/or less computational cost than recently developed operator splitting and Bregman operator splitting methods, which can deal with a general sensing matrix in reconstruction framework, to get similar or even better quality of reconstructed images.

Both acquisition and reconstruction speed are crucial for magnetic resonance (MR) imaging in clinical applications. In this paper, we present a fast reconstruction algorithm for SENSE in partially parallel MR imaging with arbitrary k-space trajectories. The proposed method is a combination of variable splitting, the classical penalty technique and the optimal gradient method. Variable splitting and the penalty technique reformulate the SENSE model with sparsity regularization as an unconstrained minimization problem, which can be solved by alternating two simple minimizations: One is the total variation and wavelet based denoising that can be quickly solved by several recent numerical methods, whereas the other one involves a linear inversion which is solved by the optimal first order gradient method in our algorithm to significantly improve the performance. Comparisons with several recent parallel imaging algorithms indicate that the proposed method significantly improves the computation efficiency and achieves state-of-the-art reconstruction quality.

In this note we present a coupled optimization model for boundary determination. One part of the model incorporates a prior shape into a geometric active contour model with a fixed parameter. The second part determines the 'best' parameter used in the first part by maximizing the mutual information of the image geometry between the prior and an aligned novel image over all the alignments that are the solutions of the first part corresponding to different parameters. We also present an alternative method, which generates an intensity model formed as the average of a set of aligned training images. Experimental results on cardiac ultrasound images are presented. These results indicate that the proposed model provides close agreement with expert traced borders, and the parameter determined in this model for one image can be used for images with similar properties. The existence of a solution to the proposed minimization problem is also discussed.