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There have been proposed several compressed imaging reconstruction algorithms for natural and MR images. In essence, however, most of them aim at the good reconstruction of edges in the images. In this paper, a nonconvex compressed sampling approach is proposed for structure-preserving image reconstruction, through imposing sparseness regularization on strong edges and also oscillating textures in images. The proposed approach can yield high-quality reconstruction as images are sampled at sampling ratios far below the Nyquist rate, due to the exploitation of a kind of approximate l0 seminorms. Numerous experiments are performed on the natural images and MR images. Compared with several existing algorithms, the proposed approach is more efficient and robust, not only yielding higher signal to noise ratios but also reconstructing images of better visual effects.

Nonconvex Compressed Sampling of Natural Images and Applications to Compressed MR Imaging