SPARTA: Sparse phase retrieval via Truncated Amplitude flow

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ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, ISSN: 1520-6149, Page: 3974-3978

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Gang Wang; Georgios B. Giannakis; Mehmet Akcakaya; Jie Chen
Institute of Electrical and Electronics Engineers (IEEE)
Computer Science; Engineering
conference paper description
A linear-time algorithm termed SPARse Truncated Amplitude flow (SPARTA) is developed for the phase retrieval (PR) of sparse signals. Upon formulating the sparse PR as a non-convex empirical loss minimization task, SPARTA emerges as an iterative solver consisting of two components: s1) a sparse orthogonality-promoting initialization leveraging support recovery and principal component analysis; and, s2) a series of refinements by hard thresholding based truncated gradient iterations. SPARTA is simple, scalable, and fast. It recovers any k-sparse n-dimensional signal (k ≪ n) of large enough minimum (in modulus) nonzero entries from about klog n measurements with high probability; this is achieved at computational complexity of order kn log n, improving upon the state-of-the-art by at least a factor of k. SPARTA is robust against bounded additive noise. Simulated tests corroborate the merits of SPARTA relative to existing alternatives.