Sublinear-Time 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 $v\in {\mathbb{R}}^n$ coordinate-wise. In this paper we present sublinear-time 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 near-optimal number of measurements.

The ell_2/ell_2 algorithm was substituted by a modification of the ell_infty/ell_2 algorithm which strictly subsumes it

References in corpus (1)

• L2/L2-foreach sparse recovery with low risk

Cited by in corpus (2)

• Sparse Phase Retrieval via Truncated Amplitude Flow
• Improved Algorithms for Adaptive Compressed Sensing