Binary and multi-bit coding for stable random projections

Ping Li

Research output: Contribution to conferencePaperpeer-review

3 Scopus citations

Abstract

The recent work [17] developed a 1-bit compressed sensing (CS) algorithm based on α-stable random projections. Although it was shown in [17] that the method is a strong competitor to other existing 1-bit CS algorithms, the procedure requires knowing K, the sparsity, which is the l0 norm of the signal. Other existing 1-bit CS algorithms require the l2 norm of the signal. In this paper, we develop an estimation procedure for the lα norm of the signal, where 0 < α ≤ 2 from binary or multi-bit measurements. We demonstrate that using a simple closed-form estimator with merely 1-bit information does not result in a significant loss of accuracy if the parameter is chosen appropriately. Theoretical tail bounds are also provided. Using 2 or more bits per measurement reduces the variance and importantly, stabilizes the estimate so that the variance is not too sensitive to chosen parameters.

Original languageAmerican English
StatePublished - Jan 1 2017
Event20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017 - Fort Lauderdale, United States
Duration: Apr 20 2017Apr 22 2017

Conference

Conference20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017
Country/TerritoryUnited States
CityFort Lauderdale
Period4/20/174/22/17

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability

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