Abstract
In this paper, we present a benchmark to sparse coding from the perspective of rank minimization. We firstly design an adaptive dictionary to bridge the gap between the group-based sparse coding (GSC) and rank minimization. Then, we prove that under the designed dictionary, GSC and the rank minimization problems are equivalent to each other, and therefore the sparse coefficients of each patch group can be measured by estimating the singular values of each patch group. Based on this scheme, we thus earn a benchmark to measure the sparsity of each patch group because the singular values of the original image patch groups can be easily computed by the singular value decomposition (SVD) operator. This benchmark can be used to evaluate the performance of any kind of norm minimization methods in sparse coding. Then, we can evaluate different norm minimization methods in sparse coding through analyzing their corresponding rank minimization counterparts. To verify the feasibility of the proposed benchmark, we compare the weighted $\ell_p$-norm minimization with the other three norm minimization methods in sparse coding. Experimental results on two image restoration applications, namely image inpainting and image compressive sensing recovery, demonstrate that the proposed scheme is feasible and outperforms many state-of-the-art methods.
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URL
https://arxiv.org/abs/1709.03979
