Sparse approximation has shown to be a significant tool in improving image restoration quality, assuming that the targeted images can be approximately sparse under some transform operators. However, it is impossible for a fixed system to be always optimal for all the images. In this paper, we present an adaptive wavelet tight frame technology for sparse representation of an image with multiplicative noise. The adaptive wavelet tight frame is first learned from the logarithmic transformed given images, and then it is used to recover these images. Compared with the existing non-adaptive wavelet sparse transform methods, the numerical results demonstrate that the proposed adaptive tight frame scheme improves image restoration quality.
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