Abstract
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.
Highlights
The compressive sensing or compressed sampling (CS) theory [1]–[3] proposed in recent years believes that, the sparse or compressible signal can be accurately reconstructed from far fewer measurements than those required by the Nyquist–Shannon sampling theorem
Inspired by the aforementioned facts, in this paper we propose to use the z-score standardization [32] to improve the sparsity of image patch groups (PGs), and by which to develop a new group sparse representation regularized image compressive sensing reconstruction (ICSR) method, called z-score standardized group sparse representation (ZSGSR) based algorithm
EXPERIMENTAL RESULTS AND ANALYSIS We conduct extensive experiments to evaluate the performance of our proposed ZSGSR based ICSR method
Summary
The compressive sensing or compressed sampling (CS) theory [1]–[3] proposed in recent years believes that, the sparse or compressible signal can be accurately reconstructed from far fewer measurements than those required by the Nyquist–Shannon sampling theorem. The estimated intermediate image is partitioned into overlapping patches, and the similar PG for each reference patch is extracted; the adaptive PCA orthogonal transformation is performed on each image PG and the z-score standardized representation of all transformation coefficients are component-wise calculated; the standardized group sparse representation is used to regularize compressed sensing reconstruction.
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