1-Bit compressed sensing of positive semi-definite matrices via rank-1 measurement matrices

Xiyuan Wang; Kun Wang; Zhongshan Zhang; Keping Long

ICASSP 2016accepted0 citations

1-Bit compressed sensing of positive semi-definite matrices via rank-1 measurement matrices

Xiyuan Wang, Kun Wang, Zhongshan Zhang, Keping Long

Abstract

In this paper, we investigate the problem of recovering positive semi-definite (PSD) matrix from 1-bit sensing. The measurement matrix is rank-1 and constructed by the outer product of a pair of vectors, whose entries are independent and identically distributed (i.i.d.) Gaussian variables. The recovery problem is solved in closed form through a convex programming. Our analysis reveals that the solution is biased in general. However, in case of error-free measurement, we find that for rank-r PSD matrix with bounded condition number, the bias decreases with an order of O(1/r). Therefore, an approximate recovery is still possible. Numerical experiments are conducted to verify our analysis.

BibTeX

@inproceedings{icassp2016_1bitcompressedse,
  title = {1-Bit compressed sensing of positive semi-definite matrices via rank-1 measurement matrices},
  author = {Xiyuan Wang and Kun Wang and Zhongshan Zhang and Keping Long},
  booktitle = {ICASSP 2016},
  year = {2016}
}