Images may be corrupted by salt and pepper impulse noise due to noisy sensors or channel transmission errors. A denoising\nmethod by detecting noise candidates and enforcing image sparsity with a patch-based sparse representation is proposed. First,\nnoise candidates are detected and an initial guide image is obtained via an adaptive median filtering; second, a patch-based sparse\nrepresentation is learnt from this guide image; third, a weighted l1-l1 regularization method is proposed to penalize the noise\ncandidates heavier than the rest of pixels. An alternating direction minimization algorithm is derived to solve the regularization\nmodel. Experiments are conducted for 30%~90% impulse noise levels, and the simulation results demonstrate that the proposed\nmethod outperforms total variation andWavelet in terms of preserving edges and structural similarity to the noise-free images.
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