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1-Bit Compressed Sensing Of Positive Semi-Definite Matrices Via Rank-1 Measurement Matrices

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.

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Paper Details

Authors:
Submitted On:
11 March 2016 - 7:32am
Short Link:
Type:
Poster
Event:
Presenter's Name:
Xiyuan Wang
Document Year:
2016
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Document Files

onebitpsdmatrecov_poster.pdf

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[1] , "1-Bit Compressed Sensing Of Positive Semi-Definite Matrices Via Rank-1 Measurement Matrices", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/611. Accessed: Jul. 05, 2020.
@article{611-16,
url = {http://sigport.org/611},
author = { },
publisher = {IEEE SigPort},
title = {1-Bit Compressed Sensing Of Positive Semi-Definite Matrices Via Rank-1 Measurement Matrices},
year = {2016} }
TY - EJOUR
T1 - 1-Bit Compressed Sensing Of Positive Semi-Definite Matrices Via Rank-1 Measurement Matrices
AU -
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/611
ER -
. (2016). 1-Bit Compressed Sensing Of Positive Semi-Definite Matrices Via Rank-1 Measurement Matrices. IEEE SigPort. http://sigport.org/611
, 2016. 1-Bit Compressed Sensing Of Positive Semi-Definite Matrices Via Rank-1 Measurement Matrices. Available at: http://sigport.org/611.
. (2016). "1-Bit Compressed Sensing Of Positive Semi-Definite Matrices Via Rank-1 Measurement Matrices." Web.
1. . 1-Bit Compressed Sensing Of Positive Semi-Definite Matrices Via Rank-1 Measurement Matrices [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/611