There have been proposed several compressed imaging reconstruction algorithms for natural and MR images. In essence, however,\r\nmost of them aim at the good reconstruction of edges in the images. In this paper, a nonconvex compressed sampling approach\r\nis proposed for structure-preserving image reconstruction, through imposing sparseness regularization on strong edges and also\r\noscillating textures in images. The proposed approach can yield high-quality reconstruction as images are sampled at sampling\r\nratios far below the Nyquist rate, due to the exploitation of a kind of approximate 0 seminorms. Numerous experiments are\r\nperformed on the natural images and MR images. Compared with several existing algorithms, the proposed approach is more\r\nefficient and robust, not only yielding higher signal to noise ratios but also reconstructing images of better visual effects.
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