Gridless Line Spectral Estimation with Phaseless Samples

Line spectral estimation is a fundamental problem in statistic signal processing. In practical scenarios, the phase information of the received samples may not be available due to hardware limitations. In this paper, we investigate the problem of line spectral estimation with phaseless samples, which is known as sparse phase retrieval under Fourier measurements. Leveraging the promising Hankel-Toeplitz model, we propose a gridless sparse algorithm based on a structured matrix embedding technique. The algorithm is implemented using the alternating direction method of multipliers. Numerical results are provided to demonstrate the superior performance of the proposed method.