A Benchmark for Sparse Coding When Group Sparsity Meets Rank Minimization


In the field of Image Processing, sparse coding has been a huge success. An image patch/group sparsity benchmark is lacking since sparse encoding is an NP-hard task. The goal of this project is to fill the void by minimising one's rank. An adaptable dictionary for bridging the gap between GSC and rank reduction is our first step. As a result of demonstrating that GSC and rank minimization issues are comparable when using a specially built dictionary, we can now estimate the singular values of each patch group in order to determine the sparse coefficients for each patch group. Singular value decomposition can be used to compute the sparsity of each patch group because the original picture patch groups can be decomposed into their singular values (SVD). With this benchmark, every sparse coding method can be tested against its corresponding rank-minimization counterpart in order to determine how well the method performs. The sparsity of each patch group is investigated using four well-known rank minimization approaches, and the weighted Schatten l p -norm minimization (WSNM) is determined to be the closest to the true singular values of each patch group. WSNM may be transformed into a non-convex weighted l p -norm minimization issue in GSC using the equivalence regime of rank minimization and GSC previously discussed. This approach is predicted to outperform the other three norm minimization methods, including the unweighted l p-norm and the two others that use the earned benchmark in sparse codification: weighted and unweighted l p-norm minimization. Weighted lp-norm minimization is compared against the three other norm minimization methods in sparse coding to ensure that the suggested benchmark is viable. Images may be restored using inpainting and compressive sensing recovery, which show that the proposed method is effective.

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