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Hessian Schatten‐norm and adaptive dictionary for image recovery
Author(s) -
Wang Qian,
Qu Gangrong,
Ji Dongjiang
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6870
Subject(s) - hessian matrix , mathematics , curvelet , compressed sensing , algorithm , norm (philosophy) , regularization (linguistics) , wavelet , minification , mathematical optimization , artificial intelligence , computer science , wavelet transform , political science , law
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.