Reweighted Atomic Norm Minimization for One-Bit Multichannel Spectral Compressed Sensing

Abstract

Multichannel spectral compressed sensing is a fundamental problem in statistical signal processing. In order to reduce the hardware cost and energy consumption, one-bit multichannel spectral compressed sensing is considered. Inspired by rewighted atomic norm minimization, we propose a new method to solve one-bit spectral compressed sensing and prove that each iteration of the proposed method is weighted atomic norm minimization. A new equivalent form of the weighted atomic norm based on Hankel-Toeplitz model is given in this paper. Numerical simulations are given to demonstrate the superior performance of the proposed method.