SublinearTime Algorithms for Compressive Phase Retrieval
Abstract
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$sparse vector $x \in \mathbb{R}^n$ given access to $y= \Phi x$, where $v$ denotes the vector obtained from taking the absolute value of $v\in\mathbb{R}^n$ coordinatewise. In this paper we present sublineartime algorithms for different variants of the compressive phase retrieval problem which are akin to the variants considered for the classical compressive sensing problem in theoretical computer science. Our algorithms use pure combinatorial techniques and nearoptimal number of measurements.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 arXiv:
 arXiv:1709.02917
 Bibcode:
 2017arXiv170902917L
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Information Theory
 EPrint:
 The ell_2/ell_2 algorithm was substituted by a modification of the ell_infty/ell_2 algorithm which strictly subsumes it