Compressed sensing MRI via fast linearized preconditioned alternating direction method of multipliers

BACKGROUND: The challenge of reconstructing a sparse medical magnetic resonance image based on compressed sensing from undersampled k-space data has been investigated within recent years. As total variation (TV) performs well in preserving edge, one type of approach considers TV-regularization as a sparse structure to solve a convex optimization problem. Nevertheless, this convex optimization problem is both nonlinear and nonsmooth, and thus difficult to handle, especially for a large-scale problem. Therefore, it is essential to develop efficient algorithms to solve a very broad class of TV-regularized problems. METHODS: In this paper, we propose an efficient algorithm referred to as the fast linearized preconditioned alternating direction method of multipliers (FLPADMM), to solve an augmented TV-regularized model that adds a quadratic term to enforce image smoothness. Because of the separable structure of this model, FLPADMM decomposes the convex problem into two subproblems. Each subproblem can be alternatively minimized by augmented Lagrangian function. Furthermore, a linearized strategy and multistep weighted scheme can be easily combined for more effective image recovery. RESULTS: The method of the present study showed improved accuracy and efficiency, in comparison to other methods. Furthermore, the experiments conducted on in vivo data showed that our algorithm achieved a higher signal-to-noise ratio (SNR), lower relative error (Rel.Err), and better structural similarity (SSIM) index in comparison to other state-of-the-art algorithms. CONCLUSIONS: Extensive experiments demonstrate that the proposed algorithm exhibits superior performance in accuracy and efficiency than conventional compressed sensing MRI algorithms.