Superset technique for approximate recovery in one-bit compressed sensing

Larkin Flodin, Venkata Gandikota, Arya Mazumdar

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations

Abstract

One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to the problem of learning a sparse hyperplane-classifier. In this paper, we propose a generic approach for signal recovery in nonadaptive 1bCS that leads to improved sample complexity for approximate recovery for a variety of signal models, including nonnegative signals and binary signals. We construct 1bCS matrices that are universal - i.e. work for all signals under a model - and at the same time recover very general random sparse signals with high probability. In our approach, we divide the set of samples (measurements) into two parts, and use the first part to recover the superset of the support of a sparse vector. The second set of measurements is then used to approximate the signal within the superset. While support recovery in 1bCS is well-studied, recovery of superset of the support requires fewer samples, which then leads to an overall reduction in sample complexity for approximate recovery.

Original languageEnglish (US)
JournalAdvances in Neural Information Processing Systems
Volume32
StatePublished - 2019
Externally publishedYes
Event33rd Annual Conference on Neural Information Processing Systems, NeurIPS 2019 - Vancouver, Canada
Duration: Dec 8 2019Dec 14 2019

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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