Compressive sensing reconstruction for compressible signal based on projection replacement

Compressive sensing can reconstruct compressible or sparse signal at the under-sampling rate. However small coefficients of the compressible signal with large number but low energy are hard to be reconstructed, while also infect the accuracy of the big coefficients. In this reason, for the compressive sensing algorithms such as orthogonal match pursuit (OMP) and tree-structed wavelet compressive sensing (TSW-CS), an assumed error is in the measurement model, which makes the reconstructed results not satisfy the original measurement model. Aiming at this problem, we propose the projection replacement (PR) algorithm by building the measurement space and its orthogonal complement space with singular value decomposition, and replacing the projection in measurement space of the reconstructed result with the pseudo-inverse one. The proposed PR algorithm eliminates the hypothetic measurement error in OMP and TSW-CS reconstructed model, and it guarantees theoretically that the PR results have a smaller error. Its effectiveness is verified experimentally with OMP and TSW-CS. The proposed algorithm serves as a good reconstruction algorithm for the CS-based applications such as image coding, super-resolution, video retrieval etc.