Eigenspace sparsity for compression and denoising

Sparsity in the eigenspace 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 redesigned to utilize such forms of sparsity and achieve improved reconstruction performance compared to existing alternatives. Relying on training data that may be noisy a novel sparsity-cognizant linear DR scheme is developed to exploit covariance-domain sparsity and form noise resilient estimates of the principal covariance eigen-basis. Norm-one regularization is used to effect sparsity, while the corresponding minimization problems are solved efficiently via coordinate decent. If data are noisy the sparsity-aware eigenspace estimator can recover a subset of the unknown signal subspace basis support when the noise power is sufficiently low. In the noiseless case the novel estimator is asymptotically normal, and the probability to identify the principal eigenspace support asymptotically approaches one.