In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the signal in question is believed to be sparse. In this paper, we use ideas from the recently developed polarization method for phase retrieval and provide an algorithm that is guaranteed to recover a sparse signal from a number of phaseless linear measurements that scales linearly with the sparsity of the signal (up to logarithmic factors). This is particularly remarkable since it is known that a certain popular class of convex methods is not able to perform recovery unless the number of measurements scales with the square of the sparsity of the signal. This is a shorter version of a more complete publication that will appear elsewhere.¹

Date Published: 26 September 2013
PDF: 10 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88581O (26 September 2013); doi: 10.1117/12.2024355

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)