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This paper considers solving the unconstrained $ell_q$-norm ($0leq q<1$) regularized least squares ($ell_q$-LS) problem for recovering sparse signals in compressive sensing. We propose two highly efficient first-order algorithms via incorporating the proximity operator for nonconvex $ell_q$-norm functions into the fast iterative shrinkage/thresholding (FISTA) and the alternative direction method of multipliers (ADMM) frameworks, respectively. Furthermore, in solving the nonconvex $ell_q$-LS problem, a sequential minimization strategy is adopted in the new algorithms to gain better global convergence performance. Unlike most existing $ell_q$-minimization algorithms, the new algorithms solve the $ell_q$-minimization problem without smoothing (approximating) the $ell_q$-norm. Meanwhile, the new algorithms scale well for large-scale problems, as often encountered in image processing. We show that the proposed algorithms are the fastest methods in solving the nonconvex $ell_q$-minimization problem, while offering competent performance in recovering sparse signals and compressible images compared with several state-of-the-art algorithms.
We consider the total variation (TV) minimization problem used for compressive sensing and solve it using the generalized alternating projection (GAP) algorithm. Extensive results demonstrate the high performance of proposed algorithm on compressive
The fundamental problem considered in this paper is What is the textit{energy} consumed for the implementation of a emph{compressive sensing} decoding algorithm on a circuit?. Using the information-friction framework, we examine the smallest amount o
Distributed Compressive Sensing (DCS) improves the signal recovery performance of multi signal ensembles by exploiting both intra- and inter-signal correlation and sparsity structure. However, the existing DCS was proposed for a very limited ensemble
Recently, it was observed that spatially-coupled LDPC code ensembles approach the Shannon capacity for a class of binary-input memoryless symmetric (BMS) channels. The fundamental reason for this was attributed to a threshold saturation phenomena der
Modern image and video compression codes employ elaborate structures existing in such signals to encode them into few number of bits. Compressed sensing recovery algorithms on the other hand use such signals structures to recover them from few linear