2018/12/17 by Sjoerd Dirksen, Shahar Mendelson, Dirksen, Sjoerd +1
Computer Science · Engineering · #Blind Source Separation Techniques #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1812.06719
openalex publication_date 2018/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present optimal sample complexity estimates for one-bit compressed sensing problems in a realistic scenario: the procedure uses a structured matrix (a randomly sub-sampled 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.