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One-Bit Compressive Sensing via Schur-Concave Function Minimization | IEEE Journals & Magazine | IEEE Xplore

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 f...Show More

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 Schur-Concave functions, 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 ℓ1 Shannon entropy function (ℓ1-SEF) is exploited. The resulting optimization problem is nonconvex. Hence, we convert it into a series of weighted ℓ1-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.
Published in: IEEE Transactions on Signal Processing ( Volume: 67, Issue: 16, 15 August 2019)
Page(s): 4139 - 4151
Date of Publication: 27 June 2019

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