ROBUST ONE-BIT COMPRESSED SENSING WITH PARTIAL CIRCULANT MATRICES

被引：6

作者：

Dirksen, Sjoerd ^{[1
]}

Mendelson, Shahar ^{[2
]}

机构：

[1] Univ Utrecht, Math Inst, Utrecht, Netherlands

[2] Australian Natl Univ, Math Sci Inst, Canberra, Australia

来源：

ANNALS OF APPLIED PROBABILITY | 2023年 / 33卷 / 03期

关键词：

Compressed sensing; quantization; random circulant matrices; empirical processes; generic chaining;

D O I：

10.1214/22-AAP1855

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured ma-trix (a randomly subsampled circulant matrix) and is robust to analog pre -quantization 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.

引用

页码：1874 / 1903

页数：30

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