Image restoration by minimizing zero norm of wavelet frame coefficients. (20th September 2016)

• Record Type: Journal Article
• Authors: Bao, Chenglong; Dong, Bin; Hou, Likun; Shen, Zuowei; Zhang, Xiaoqun; Zhang, Xue
• Is Part Of: Inverse problems. Volume 32:Number 11(2016:Nov.)
• Publication Date: 2016-09-20
• Subjects: wavelet frame -- iterative hard threshholding -- ℓ0 regularization -- local minimizer; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/11/115004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the ℓ 0 -norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka–Łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of ℓ 0 -norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.