Multi-source phase retrieval from multi-channel phaseless STFT measurements

In a recent study, it was shown that, given only the magnitude of the short-time Fourier transform (STFT) of a signal, it is possible to recover the phase information of its STFT under certain conditions. However, this is only investigated for the single-source scenario. In this paper, we extend this work and formulate a multi-source phase retrieval problem where multi-channel phaseless STFT measurements are given as input. We then present a robust multi-source phase retrieval (RMSPR) algorithm based on a gradient descent (GD) algorithm by minimizing a non-convex loss function and independent component analysis (ICA). An improved least squares (LS) loss function is presented to find the initialization of the GD algorithm. Experimental evaluation has been conducted to show that under appropriate conditions the proposed algorithm can explicitly recover the phase of the sources, the mixing matrix, and the sources simultaneously, from noisy measurements.