Abstract
Sparsity in the eigenvectors of signal covariance matrices is exploited in this paper for compression and denoising. Dimensionality reduction (DR) and quantization modules present in many practical compression schemes such as transform codecs, are designed to capitalize on this form of sparsity and achieve improved reconstruction performance compared to existing sparsity-agnostic codecs. Using training data that may be noisy a novel sparsity-aware linear DR scheme is developed to fully exploit sparsity in the covariance eigenvectors and form noise-resilient estimates of the principal covariance eigenbasis. Sparsity is effected via norm-one regularization, and the associated minimization problems are solved using computationally efficient coordinate descent iterations. The resulting eigenspace estimator is shown capable of identifying a subset of the unknown support of the eigenspace basis vectors even when the observation noise covariance matrix is unknown, as long as the noise power is sufficiently low. It is proved that the sparsity-aware estimator is asymptotically normal, and the probability to correctly identify the signal subspace basis support approaches one, as the number of training data grows large. Simulations using synthetic data and images, corroborate that the proposed algorithms achieve improved reconstruction quality relative to alternatives.
Original language | English (US) |
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Article number | 6140983 |
Pages (from-to) | 2408-2421 |
Number of pages | 14 |
Journal | IEEE Transactions on Signal Processing |
Volume | 60 |
Issue number | 5 |
DOIs | |
State | Published - May 2012 |
Bibliographical note
Funding Information:Manuscript received October 07, 2010; revised July 05, 2011 and November 13, 2011; accepted January 07, 2012. Date of publication January 26, 2012; date of current version April 13, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Maja Bystrom. The work in this paper was supported by NSF Grant CCF-1016605. Part of the paper was presented in the Third International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Aruba, Dutch Antilles, December 2009.
Keywords
- Data compression
- PCA
- denoising
- quantization
- subspace estimation