Vehkapera, M.T., Kabashima, Y. and Chatterjee, S. (2016) Analysis of Regularized LS Reconstruction and Random Matrix Ensembles in Compressed Sensing. IEEE Transactions on Information Theory. ISSN 0018-9448
Abstract
Performance of regularized least-squares estimation in noisy compressed sensing is analyzed in the limit when the dimensions of the measurement matrix grow large. The sensing matrix is considered to be from a class of random ensembles that encloses as special cases standard Gaussian, row-orthogonal, geometric and so-called T-orthogonal constructions. Source vectors that have non-uniform sparsity are included in the system model. Regularization based on l1-norm and leading to LASSO estimation, or basis pursuit denoising, is given the main emphasis in the analysis. Extensions to l2-norm and "zero-norm" regularization are also briefly discussed. The analysis is carried out using the replica method in conjunction with some novel matrix integration results. Numerical experiments for LASSO are provided to verify the accuracy of the analytical results. The numerical experiments show that for noisy compressed sensing, the standard Gaussian ensemble is a suboptimal choice for the measurement matrix. Orthogonal constructions provide a superior performance in all considered scenarios and are easier to implement in practical applications. It is also discovered that for non-uniform sparsity patterns the T-orthogonal matrices can further improve the mean square error behavior of the reconstruction when the noise level is not too high. However, as the additive noise becomes more prominent in the system, the simple row-orthogonal measurement matrix appears to be the best choice out of the considered ensembles.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Electronic and Electrical Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Feb 2016 12:56 |
Last Modified: | 31 Mar 2018 17:00 |
Published Version: | http://dx.doi.org/10.1109/TIT.2016.2525824 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Refereed: | Yes |
Identification Number: | 10.1109/TIT.2016.2525824 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:94762 |