A New Non-Convex Regularized Sparse Reconstruction Algorithm for Compressed Sensing Magnetic Resonance Image Recovery

Abstract

Compressed sensing (CS) relies on the sparse priorin posed on the signal to solve the ill-posed recovery problem in an under-determined linear system (ULS). Motivated by the theory, this paper proposes a new algorithm called regularized re-weighted inverse trigonometric smoothed function approximating L 0-norm minimization (RRITSL0) algorithm, where the inverse trigonometric (IT) function, iteratively re-weighted scheme and regularization mechanism constitute the core of the proposed RRITSL0 algorithm. Compared with other state-of-the-art functions, our proposed IT function cluster can better approximate the L 0-norm, thus improving the reconstruction accuracy. And the new re-weighted scheme we adopted can promote sparsity and speed up convergence. Moreover, the regularization mechanism makes the RRITSL0 algorithm more robust against noise. The performance of the proposed algorithm is verified via numerical experiments with additive noise. Furthermore, the experiments prove the superiority of the RRITSL0 algorithm in magnetic resonance (MR) image recovery.

An Iterative Threshold Algorithm Based on Log-Sum Norm Regularization for Magnetic Resonance Image Recovery

“…Paper [7] proposes to apply l 1 2 norm to iterative threshold algorithm, which further extends the compressed sensing algorithm. Now, this kind of compressed sensing algorithm is widely used in various fields, such as image restoration [8][9][10] and MRI imaging [11], because of its strong scalability.…”

A Smoothed l0-Norm and l1-Norm Regularization Algorithm for Computed Tomography

“…0 -norm regularization model is proposed for sparse-view X-ray CT reconstruction [10]. Two new smoothed functions approximating the 0 -norm are proposed in the mechanism of reweighted regularization 2 Journal of Applied Mathematics [11,12]. An edge-preserving image reconstruction method based on 0 -regularized gradient prior for limited-angle CT is investigated [13].…”