Paper Info
Title
To average or not to average: Trade-off in compressed sensing with noisy measurements
Abstract
We consider the situation where the total number of measurements is limited in compressed sensing of sparse vectors with noisy measurements. In this situation there is a trade-off between acquiring as many independent observations as possible and performing averaging over several identical measurements in order to improve signal-to-noise ratio. With the help of the approximate message passing algorithm to solve LASSO problems, we have proved, via state evolution, that in order to minimize estimation errors one should perform as many independent linear measurements as possible rather than performing averaging to improve signal-to-noise ratio of the observations. Furthermore, we have confirmed via numerical experiments that the same holds in the case where the measurement matrix is constructed by randomly subsampling rows of a discrete Fourier matrix.
Year
DOI
Venue
2014
10.1109/ISIT.2014.6875046
Information Theory
Keywords
Field
DocType
approximation theory,compressed sensing,matrix algebra,message passing,vectors,LASSO problems,approximate message passing algorithm,compressed sensing,discrete Fourier matrix,independent linear measurements,measurement matrix,noisy measurements,signal-to-noise ratio improvement,sparse vectors
Computer science,Theoretical computer science,Compressed sensing
Conference
Citations 
PageRank 
References 
0
0.34
5
Authors
3
Name
Order
Citations
PageRank
Sano, K.100.34
Matsushita, Ryosuke261.83
Toshiyuki Tanaka319019.98