Multilevel Subsampling of Principal Component Projections for Adaptive Compressive Sensing

Abstract

bstract-This paper examines the performance of principal-component-analysis (PCA) projections in compressive sensing (CS). Observed signals are assumed to follow a Gaussian distribution and have the asymptotic sparsity property in a wavelet transform domain. In order to exploit these signal priors, we propose multilevel subsampling of PCA projections in addition to sparsity-promoting $l$ 1 regularization. The PCA projections are subsampled in levels that correspond to different wavelet scales. The proposed method outperforms universal random projections of standard CS for noise-corrupted measurement setups and compressible signals. Experimental results from simulations conducted on images from the MNIST dataset prove the framework's robustness and good reconstruction ability.