One-Bit ExpanderSketch for One-Bit Compressed Sensing

TL;DR

This paper introduces a novel one-bit expander sketch that enables efficient approximate recovery of sparse vectors with fewer measurements and faster decoding, advancing the state of one-bit compressed sensing.

Contribution

It presents the first scheme achieving near-optimal measurements and sublinear decoding time for non-uniform one-bit compressed sensing.

Findings

Achieves almost optimal measurements for sparse recovery

Provides sublinear decoding time

Improves previous bounds in measurements and decoding speed

Abstract

Is it possible to obliviously construct a set of hyperplanes H such that you can approximate a unit vector x when you are given the side on which the vector lies with respect to every h in H? In the sparse recovery literature, where x is approximately k-sparse, this problem is called one-bit compressed sensing and has received a fair amount of attention the last decade. In this paper we obtain the first scheme that achieves almost optimal measurements and sublinear decoding time for one-bit compressed sensing in the non-uniform case. For a large range of parameters, we improve the state of the art in both the number of measurements and the decoding time.