Image reconstruction with locally adaptive sparsity and nonlocal robust regularization |
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Authors: | Weisheng Dong Guangming Shi Xin Li Lei Zhang Xiaolin Wu |
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Affiliation: | 1. Key Laboratory of Intelligent Perception and Image Understanding (Chinese Ministry of Education), School of Electronic Engineering, Xidian University, Xi''an, China;2. Lane Dept. of Comp. Sci. and Elec. Engr., West Virginia University, Morgantown, WV 26506, USA;3. Dept. of Computing, The Hong Kong Polytechnic University, Kowloon, Hong Kong;4. Dept. of Electrical and Computer Engineering, McMaster University, ON, Canada;1. Department of Electrical and Electronic Engineering, University of Cagliari, 09123 Cagliari, Italy;2. Multimedia Communications Laboratory, CNIT, 09010 Pula, Italy;1. Electrical and Computer Eng. Dept., University of British Columbia, Vancouver, BC, Canada;2. Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran;1. Department of Information Science, School of Mathematical Sciences and LMAM, Peking University, Beijing 100871, China;2. Electronic Information Engineering College, Henan University of Science and Technology, Luoyang 471023, China |
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Abstract: | Sparse representation based modeling has been successfully used in many image-related inverse problems such as deblurring, super-resolution and compressive sensing. The heart of sparse representations lies on how to find a space (spanned by a dictionary of atoms) where the local image patch exhibits high sparsity and how to determine the image local sparsity. To identify the locally varying sparsity, it is necessary to locally adapt the dictionary learning process and the sparsity-regularization parameters. However, spatial adaptation alone runs into the risk of over-fitting the data because variation and invariance are two sides of the same coin. In this work, we propose two sets of complementary ideas for regularizing image reconstruction process: (1) the sparsity regularization parameters are locally estimated for each coefficient and updated along with adaptive learning of PCA-based dictionaries; (2) a nonlocal self-similarity constraint is introduced into the overall cost functional to improve the robustness of the model. An efficient alternative minimization algorithm is present to solve the proposed objective function and then an effective image reconstruction algorithm is presented. The experimental results on image deblurring, super-resolution and compressive sensing demonstrate that the proposed image reconstruct method outperforms many existing image reconstruction methods in both PSNR and visual quality assessment. |
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