Title
Asymptotic analysis of complex LASSO via complex approximate message passing (CAMP)
Author
Maleki, A.
Anitori, L.
Yang, Z.
Baraniuk, R.G.
Publication year
2013
Abstract
Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex-valued. We study the popular recovery method of l1- regularized least squares or LASSO.While several studies have shown that LASSO provides desirable solutions under certain conditions, the precise asymptotic performance of this algorithm in the complex setting is not yet known. In this paper, we extend the approximate message passing (AMP) algorithm to solve the complex-valued LASSO problem and obtain the complex approximate message passing algorithm (CAMP). We then generalize the state evolution framework recently introduced for the analysis of AMP to the complex setting. Using the state evolution, we derive accurate formulas for the phase transition and noise sensitivity of both LASSO and CAMP. Our theoretical results are concerned with the case of i.i.d. Gaussian sensing matrices. Simulations confirm that our results hold for a larger class of random matrices. © 2013 IEEE.
Subject
Physics & Electronics
RT - Radar Technology
TS - Technical Sciences
Defence Research
Informatics
Defence, Safety and Security
Approximate message passing (AMP)
Complexvalued LASSO
Compressed sensing (CS)
Minimax analysis
Linear measurements
Message passing algorithm
Regularized least squares
Algorithms
Asymptotic analysis
Signal reconstruction
Matrix algebra
To reference this document use:
http://resolver.tudelft.nl/uuid:59818010-6945-4b95-999a-d5f12d688020
DOI
https://doi.org/10.1109/tit.2013.2252232
TNO identifier
500194
Source
IEEE Transactions on Information Theory, 59 (7), 4290-4308
Document type
article