Gridless compressive sensing method for line spectral estimation from 1-bit measurements

Abstract This paper considers the problem of recovering frequency sparse signals which consist of a few complex sinusoids and estimating the frequency components from 1-bit quantized measurements. Unlike previous grid-based 1-bit compressive sensing approaches, we present a gridless convex method to recover frequency sparse signals form 1-bit measurements via binary atomic norm minimization (BANM). And the frequencies can take any continuous values in the frequency domain, which overcomes grid mismatches caused by the off-grid problem. We further propose a dual polynomial method to achieve continuous frequency estimation. Moreover, we present an efficient algorithm to solve BANM for large scaled problem. Numerical experiments are performed to demonstrate the effectiveness of our method compared with the grid-based compressive sensing algorithm.