Hessian Schatten‐norm and adaptive dictionary for image recovery. (14th September 2020)

• Record Type: Journal Article
• Authors: Wang, Qian; Qu, Gangrong; Ji, Dongjiang
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 2(2021)
• Page Start: 1674
• Page End: 1687
• Publication Date: 2020-09-14
• Subjects: adaptive dictionary -- compressed sensing -- image recovery -- Hessian Schatten‐norm -- sparse representation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6870
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : From many fewer acquired measurements than that suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that a signal can be reconstructed with high probability when it exhibits sparsity in a certain domain. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel algorithm for image recovery, which minimizes a linear combination of three terms corresponding to least square data fitting, adaptive dictionary, and Hessian Schatten‐norm regularization. We split the problem into some subproblems which turn the minimization task into much simpler. Numerical experiments are conducted on several test images with a variety of sampling patterns and ratios in both noiseless and noise scenarios. The results demonstrate the superior performance of the proposed algorithm.