Efficient Compressed Sensing Based MRI Reconstruction using Nonconvex Total Variation Penalties

6th International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Lazzaro, D.^1 ; Piccolomini, E. Loli^1 ; Zama, F.^1

Department of Mathematics, University of Bologna, Italy^1

关键词: Adaptive adjustment;    Constrained minimization problem;    Constrained problem;    Continuation techniques;    Iterative algorithm;    Nonconvex functions;    Numerical experiments;    Objective functions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/756/1/012004/pdf
DOI  :  10.1088/1742-6596/756/1/012004

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

This work addresses the problem of Magnetic Resonance Image Reconstruction from highly sub-sampled measurements in the Fourier domain. It is modeled as a constrained minimization problem, where the objective function is a non-convex function of the gradient of the unknown image and the constraints are given by the data fidelity term. We propose an algorithm, Fast Non Convex Reweighted (FNCR), where the constrained problem is solved by a reweighting scheme, as a strategy to overcome the non-convexity of the objective function, with an adaptive adjustment of the penalization parameter. We propose a fast iterative algorithm and we can prove that it converges to a local minimum because the constrained problem satisfies the Kurdyka-Lojasiewicz property. Moreover the adaptation of non convex l0 approximation and penalization parameters, by means of a continuation technique, allows us to obtain good quality solutions, avoiding to get stuck in unwanted local minima. Some numerical experiments performed on MRI sub-sampled data show the efficiency of the algorithm and the accuracy of the solution.