SparsePR (Sparse Phase Retrieval)

This MATLAB package includes implementations of a fast second-order algorithm that utilizes a Newton-type method with hard thresholding for sparse phase retrieval, as proposed in [1].

The algorithm consists of two stages:

1. Initialization: The first stage generates an initial estimate that is close to the ground truth signal, using the sparse spectral initialization method proposed in [2].

2. Refinement: The second stage refines the initial estimate to obtain the ground truth signal, using our proposed second-order algorithm.

To run the code:

(1) Download the source files. (2) Run 'demo.m' in MATLAB.

References

[1] Jian-Feng Cai, Yu Long, Ruixue Wen, and Jiaxi Ying, "A Fast and Provable Algorithm for Sparse Phase Retrieval", in International Conference on Learning Representations (ICLR), 2024.

[2] Gauri Jagatap, and Chinmay Hegde, "Sample-Efficient Algorithms for Recovering Structured Signals From Magnitude-Only Measurements," in IEEE Transactions on Information Theory, vol. 65, no. 7, pp. 4434-4456, July 2019.