Sparse Signal Phase Retrieval for Phaseless Short-Time Fourier Transform Measurement Based on Local Search

The sparse signal phase retrieval (PR) for phaseless short-time Fourier transform (STFT) measurement is a crucial problem manifesting across various applications. The existing solutions involve amplitude and support estimation. Amplitude estimation, a nonlinear least squares problem, faces issues due to the not full rank of the derivative matrix associated with the objective function. Existing support estimation relies on random initialization, reducing accuracy and noise robustness. To address these, a novel phaseless measurement structure and the corresponding solution framework are proposed. Initially, a measurements preprocessing algorithm is employed, utilizing the properties of the measurement matrix to efficiently reduce the dimensions of the solution. Subsequently, a support estimation algorithm based on local search is developed, where the support preestimation takes advantage of the sparse support characteristics. In addition, an amplitude estimation algorithm, utilizing the trust region method, is proposed. The proposed algorithm's effectiveness and its superiority in accuracy and noise robustness over existing methods are demonstrated through numerical simulations and hardware experiments.