A Weighted Two-Level Bregman Method with Dictionary Updating for Nonconvex MR Image Reconstruction

Nonconvex optimization has shown that it needs substantially fewer measurements than l1 minimization for exact recovery under fixed transform/overcomplete dictionary. In this work, two efficient numerical algorithms which are unified by the method named weighted two-level Bregman method with dictionary updating (WTBMDU) are proposed for solving lp optimization under the dictionary learning model and subjecting the fidelity to the partial measurements. By incorporating the iteratively reweighted norm into the two-level Bregman iteration method with dictionary updating scheme (TBMDU), the modified alternating direction method (ADM) solves the model of pursuing the approximated lp-norm penalty efficiently. Specifically, the algorithms converge after a relatively small number of iterations, under the formulation of iteratively reweighted l1 and l2 minimization. Experimental results on MR image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed method can efficiently reconstruct MR images from highly undersampled k-space data and presents advantages over the current state-of-the-art reconstruction approaches, in terms of higher PSNR and lower HFEN values

Parallel MR Image Reconstruction Using Augmented Lagrangian Methods

Magnetic resonance image (MRI) reconstruction using SENSitivity Encoding (SENSE) requires regularization to suppress noise and aliasing effects. Edge-preserving and sparsity-based regularization criteria can improve image quality, but they demand computation-intensive nonlinear optimization. In this paper, we present novel methods for regularized MRI reconstruction from undersampled sensitivity encoded data-SENSE-reconstruction-using the augmented Lagrangian (AL) framework for solving large-scale constrained optimization problems. We first formulate regularized SENSE-reconstruction as an unconstrained optimization task and then convert it to a set of (equivalent) constrained problems using variable splitting. We then attack these constrained versions in an AL framework using an alternating minimization method, leading to algorithms that can be implemented easily. The proposed methods are applicable to a general class of regularizers that includes popular edge-preserving (e.g., total-variation) and sparsity-promoting (e.g., -norm of wavelet coefficients) criteria and combinations thereof. Numerical experiments with synthetic and in vivo human data illustrate that the proposed AL algorithms converge faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85846/1/Fessler4.pd

Image Reconstructions of Compressed Sensing MRI with Multichannel Data

Magnetic resonance imaging (MRI) provides high spatial resolution, high-quality of soft-tissue contrast, and multi-dimensional images. However, the speed of data acquisition limits potential applications. Compressed sensing (CS) theory allowing data being sampled at sub-Nyquist rate provides a possibility to accelerate the MRI scan time. Since most MRI scanners are currently equipped with multi-channel receiver systems, integrating CS with multi-channel systems can further shorten the scan time and also provide a better image quality. In this dissertation, we develop several techniques for integrating CS with parallel MRI. First, we propose a method which extends the reweighted l1 minimization to the CS-MRI with multi-channel data. The individual channel images are recovered according to the reweighted l1 minimization algorithm. Then, the final image is combined by the sum-of-squares method. Computer simulations show that the new method can improve the reconstruction quality at a slightly increased computation cost. Second, we propose a reconstruction approach using the ubiquitously available multi-core CPU to accelerate CS reconstructions of multiple channel data. CS reconstructions for phase array system using iterative l1 minimization are significantly time-consuming, where the computation complexity scales with the number of channels. The experimental results show that the reconstruction efficiency benefits significantly from parallelizing the CS reconstructions, and pipelining multi-channel data on multi-core processors. In our experiments, an additional speedup factor of 1.6 to 2.0 was achieved using the proposed method on a quad-core CPU. Finally, we present an efficient reconstruction method for high-dimensional CS MRI with a GPU platform to shorten the time of iterative computations. Data managements as well as the iterative algorithm are properly designed to meet the way of SIMD (single instruction/multiple data) parallelizations. For three-dimension multi-channel data, all slices along frequency encoding direction and multiple channels are highly parallelized and simultaneously processed within GPU. Generally, the runtime on GPU only requires 2.3 seconds for reconstructing a simulated 4-channel data with a volume size of 256×256×32. Comparing to 67 seconds using CPU, it achieves 28 faster with the proposed method. The rapid reconstruction algorithms demonstrated in this work are expected to help bring high dimensional, multichannel parallel CS MRI closer to clinical applications