A Weighted Convex Optimized Phase Retrieval Method for Short-Time Fourier Transform Measurement With Outliers

As a problem of reconstructing the original signal from phaseless short-time Fourier transform (STFT) measurement, STFT phase retrieval (PR) is widespread in many fields. The existing PR algorithms for STFT measurement can uniquely determine the original signal (up to a global phase), however they are invalid when outlier interference exists. Aiming at this problem, we propose a weighted convex optimization PR method by introducing a weight matrix that can identify outliers. Meanwhile, a two-channel phaseless measurement structure based on the mask technique and the corresponding calculation algorithm are proposed to obtain the weight matrix. In particular, by accumulating the measurement results of all short-time segments, the support of outliers can be well identified in the weight matrix calculation. Simulation and hardware experiments demonstrate the performance improvement of the proposed approach compared to the existing methods, which shows its effectiveness in suppressing outlier interference.