June 2023 Robust one-bit compressed sensing with partial circulant matrices
Sjoerd Dirksen, Shahar Mendelson
Author Affiliations +
Ann. Appl. Probab. 33(3): 1874-1903 (June 2023). DOI: 10.1214/22-AAP1855


We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly subsampled circulant matrix) and is robust to analog prequantization noise as well as to adversarial bit corruptions in the quantization process. Our results imply that quantization is not a statistically expensive procedure in the presence of nontrivial analog noise: recovery requires the same sample size one would have needed had the measurement matrix been Gaussian and the noisy analog measurements been given as data.

Funding Statement

SD acknowledges funding from the DFG through the project Quantized Compressive Spectrum Sensing (QuaCoSS) which is part of the Priority Program SPP 1798 Compressive Sensing in Information Processing (COSIP).


The authors would like to thank the anonymous reviewer and the associate editor for their helpful comments on this article.


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Sjoerd Dirksen. Shahar Mendelson. "Robust one-bit compressed sensing with partial circulant matrices." Ann. Appl. Probab. 33 (3) 1874 - 1903, June 2023. https://doi.org/10.1214/22-AAP1855


Received: 1 March 2020; Revised: 1 April 2022; Published: June 2023
First available in Project Euclid: 2 May 2023

MathSciNet: MR4583660
zbMATH: 1515.94023
Digital Object Identifier: 10.1214/22-AAP1855

Primary: 60B20 , 94A12

Keywords: compressed sensing , Empirical processes , generic chaining , quantization , random circulant matrices

Rights: Copyright © 2023 Institute of Mathematical Statistics


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Vol.33 • No. 3 • June 2023
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