Sparse Signal Inversion with Impulsive Noise by Dual Spectral Projected Gradient Method

作者：Ding, Liang^*; Zhao, Hui; Dou, Yixin

来源：Mathematical Problems in Engineering, 2017, 2017: 2736306.

DOI：10.1155/2017/2736306

• ALTERNATING DIRECTION ALGORITHMS
• CONVERGENCE-RATES
• REGULARIZATION
• MINIMIZATION
• MINIMIZERS
• RECOVERY
• MODEL

We consider sparse signal inversion with impulsive noise. There are three major ingredients. The first is regularizing properties; we discuss convergence rate of regularized solutions. The second is devoted to the numerical solutions. It is challenging due to the fact that both fidelity and regularization term lack differentiability. Moreover, for ill-conditioned problems, sparsity regularization is often unstable. We propose a novel dual spectral projected gradient (DSPG) method which combines the dual problem of multiparameter regularization with spectral projection gradient method to solve the nonsmooth l(1) + l(1) optimization functional. We show that one can overcome the nondifferentiability and instability by adding a smooth l(2) regularization term to the original optimization functional. The advantage of the proposed functional is that its convex duality reduced to a constraint smooth functional. Moreover, it is stable even for ill-conditioned problems. Spectral projected gradient algorithm is used to compute the minimizers and we prove the convergence. The third is numerical simulation. Some experiments are performed, using compressed sensing and image inpainting, to demonstrate the efficiency of the proposed approach.

• 出版日期2017
• 单位哈尔滨商业大学; 东北林业大学