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 k2 log n measurements with high probability; this is achieved at computational complexity of order k2n 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.
|Original language||English (US)|
|Title of host publication||2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||5|
|State||Published - Jun 16 2017|
|Event||2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States|
Duration: Mar 5 2017 → Mar 9 2017
|Name||ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings|
|Other||2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017|
|Period||3/5/17 → 3/9/17|
Bibliographical noteFunding Information:
Work in this paper was supported in part by NSF grants 1500713 and 1514056.
© 2017 IEEE.
Copyright 2017 Elsevier B.V., All rights reserved.
- Nonconvex optimization
- hard thresholding
- linear convergence
- support recovery