Trust, but verify: Fast and accurate signal recovery from 1-Bit compressive measurements

Jason N. Laska, Zaiwen Wen, Wotao Yin, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

141 Scopus citations


The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. This property enables the design of simplified CS acquisition hardware based around a simple sign comparator rather than a more complex analog-to-digital converter; moreover, it ensures robustness to gross nonlinearities applied to the measurements. In this paper we introduce a new algorithmrestricted-step shrinkage (RSS)to recover sparse signals from 1-bit CS measurements. In contrast to previous algorithms for 1-bit CS, RSS has provable convergence guarantees, is about an order of magnitude faster, and achieves higher average recovery signal-to-noise ratio. RSS is similar in spirit to trust-region methods for nonconvex optimization on the unit sphere, which are relatively unexplored in signal processing and hence of independent interest.

Original languageEnglish (US)
Article number5955138
Pages (from-to)5289-5301
Number of pages13
JournalIEEE Transactions on Signal Processing
Issue number11
StatePublished - Nov 2011


  • 1-Bit compressive sensing
  • consistent reconstruction
  • quantization
  • trust-region algorithms

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing


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