Abstract
Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction.
Highlights
Compressive sensing (CS) [1, 2] allows us to reconstruct high dimensional data with only a small number of samples or measurements, and captures only useful information and has the potential of significantly improving the energy efficiency of sensors in the real-world applications
Before deriving rf(Á), we show the gradient of smoothed rank function (SRF) Gδ(Li) at Li [30] as follows: rGdðLiÞ 1⁄4 ÀUdiag where matrixes U and V and singular values σi (i = 1, Á Á Á, l) come from the singular value decomposition (SVD) of Li, which is obtained in previous iteration, Li 1⁄4 Udiagðs1; Á Á Á ; s‘ÞVT: ð15Þ
To better exploit the nonlocal sparsity of similar patches and non-convexity of rank minimization, in this paper, we use the non-convex SRF function surrogating the rank as a low-rank regularization for CS image recovery
Summary
OPEN ACCESS Citation: Fan Y-R, Huang T-Z, Liu J, Zhao X-L (2016) Compressive Sensing via Nonlocal Smoothed Rank Function. Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction. Editor: Pew-Thian Yap, University of North Carolina at Chapel Hill, UNITED STATES.
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