Sparse Phase Retrieval for Clustered-Sparse Signals: A Graph Cut-Based Truncated Flow Approach

This paper proposes a robust graph cut truncated flow (GCTF) algorithm to tackle the clustered-sparse phase retrieval problem. The GCTF algorithm is an iterative algorithm, which comprises three modules: 1) Deriving the rough estimate via the gradient-descent method; 2) Truncating the rough estimate via graph cut; 3) Refining the estimate based on the reduced measurement matrix. Compared with the existing algorithms, our proposed GCTF features three significant advantages: (i) Applicability to arbitrary graph topologies. (ii) No need for any prior beyond clustered sparsity. (iii) Robustness under relatively low signal-to-noise ratio (SNR) levels. Experimental results are presented to demonstrate the fidelity of the GCTF algorithm, especially its great robustness under relatively low SNR levels.