Title
One-Bit Compressive Sensing via Schur-Concave Function Minimization
Abstract
Much effort has been devoted to recovering sparse signals from one-bit measurements in recent years. However, it is still quite challenging to recover signals with high fidelity, which is desired in practical one-bit compressive sensing (1-bit CS) applications. We introduce the notion of Schur-concavity in this paper and propose to construct signals by taking advantage of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Schur-Concave functions</italic> , which are capable of enhancing sparsity. Specifically, the Schur-concave functions can be employed to measure the degree of concentration, and the sparse solutions are obtained at the minima. As a representative of the Schur-concave family, the normalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula> Shannon entropy function ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula> -SEF) is exploited. The resulting optimization problem is nonconvex. Hence, we convert it into a series of weighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\ell _1}$</tex-math></inline-formula> -norm subproblems, which are solved iteratively by a generalized fixed-point continuation algorithm. Numerical results are provided to illustrate the effectiveness and superiority of the proposed 1-bit CS algorithm.
Year
DOI
Venue
2019
10.1109/TSP.2019.2925606
IEEE Transactions on Signal Processing
Keywords
DocType
Volume
Signal processing algorithms,Entropy,Noise measurement,Minimization,Atmospheric measurements,Particle measurements,Compressed sensing
Journal
67
Issue
ISSN
Citations 
16
1053-587X
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Peng Xiao15013.83
Bin Liao219632.33
Jian Li31643147.83