Multiple Input Single Output Phase Retrieval

Abstract

In this paper, we consider the problem of recovering the phase information of multiple sources from a mixed phaseless Short-Time Fourier Transform (STFT) measurement, which is called multiple input single output (MISO) phase retrieval problem. It is an inherently ill-posed problem due to the lack of the phase and mixing information, and the existing phase retrieval algorithms are not explicitly designed for this case. To address the MISO phase retrieval problem, a least squares (LS) method coupled with an independent component analysis (ICA) algorithm is proposed for the case of sufficiently long window length. When these conditions are not met, an integrated algorithm is presented, which combines a gradient descent (GD) algorithm by minimizing a non-convex loss function with an ICA algorithm. Experimental evaluation has been conducted to show that under appropriate conditions the proposed algorithms can explicitly recover the signals, the phases of the signals and the mixing matrix. In addition, the algorithm is robust to noise