An accelerated majorization-minimization algorithm with convergence guarantee for non-Lipschitz wavelet synthesis model*Submitted to the editors DATE. (6th December 2021)

• Record Type: Journal Article
• Authors: Zhao, Yanan; Wu, Chunlin; Dong, Qiaoli; Zhao, Yufei
• Is Part Of: Inverse problems. Volume 38:Number 1(2022)
• Publication Date: 2021-12-06
• Subjects: ℓpregularization -- Isoft algorithm -- extrapolation -- support shrinking -- Kurdyka–Łojasiewicz property -- wavelet frames; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac38b8
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider a wavelet based image reconstruction model with the ℓ p (0 < p < 1) quasi-norm regularization, which is a non-convex and non-Lipschitz minimization problem. For solving this model, Figueiredo et al (2007 IEEE Trans. Image Process. 16 2980–2991) utilized the classical majorization-minimization framework and proposed the so-called Isoft algorithm. This algorithm is computationally efficient, but whether it converges or not has not been concluded yet. In this paper, we propose a new algorithm to accelerate the Isoft algorithm, which is based on Nesterov's extrapolation technique. Furthermore, a complete convergence analysis for the new algorithm is established. We prove that the whole sequence generated by this algorithm converges to a stationary point of the objective function. This convergence result contains the convergence of Isoft algorithm as a special case. Numerical experiments demonstrate good performance of our new algorithm.