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Restoration of images and 3D data to higher resolution by deconvolution with sparsity regularization

8 years 8 months ago
Restoration of images and 3D data to higher resolution by deconvolution with sparsity regularization
Image convolution is conventionally approximated by the LTI discrete model. It is well recognized that the higher the sampling rate, the better is the approximation. However sometimes images or 3D data are only available at a lower sampling rate due to physical constraints of the imaging system. In this paper, we model the under-sampled observation as the result of combining convolution and subsampling. Because the wavelet coefficients of piecewise smooth images tend to be sparse and well modelled by tree-like structures, we propose the L0 reweighted-L2 minimization (L0RL2 ) algorithm to solve this problem. This promotes model-based sparsity by minimizing the reweighted L2 norm, which approximates the L0 norm, and by enforcing a tree model over the weights. We test the algorithm on 3 examples: a simple ring, the cameraman image and a 3D microscope dataset; and show that good results can be obtained.
Yingsong Zhang, Nick G. Kingsbury
Added 12 Feb 2011
Updated 12 Feb 2011
Type Journal
Year 2010
Where ICIP
Authors Yingsong Zhang, Nick G. Kingsbury
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