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
收藏
页码：1874 / 1903
页数：30
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