Image Compressive Sensing Reconstruction Based on z-Score Standardized Group Sparse Representation

Non-local similarity-based group sparse representation (GSR) has shown great potential in image restoration. Considering the universal existing non-stationarity of natural images and the statistic characteristic differences of different components in the sparse domain of image patch group, this paper proposes a new image compressive sensing reconstruction (ICSR) algorithm based on z-score standardized group sparse representation (ZSGSR). Specifically, the image is first partitioned into overlapping patches, and the similar patch groups are further generated to be decomposed by adaptive PCA dictionary; then, the resulting sparse coefficients are performed component-wise on z-score standardization; finally, the l
₁
norm of the standardized sparse coefficients are used to regularize the ICSR. The reconstruction model is solved by splitting Bregman iteration (SBI) and soft threshold shrinking algorithms. The z-score standardization could enhance sparse representation ability, which reflects the importance of different sparse coefficients well; this is beneficial to effectively preserve the crucial small coefficients and to better recovery, the edges and texture details of images, thus improving the reconstructed image quality. Using objective and subjective quality evaluation, the extensive experiments show that the proposed method can obtain a better performance than the existing state-of-the-art algorithms.