Compressive Covariance Sensing: Structure-Based Compressive Sensing Beyond Sparsity - Daniel Romero; Dyonisius D Ariananda; Zhi Tian; Geert Leus (IEEE Signal Processing Magazine, 2016)
Compressed sensing deals with the reconstruction of signals from sub-Nyquist samples by exploiting the sparsity of their projections onto known subspaces. In contrast, the present article is concerned with the reconstruction of second-order statistics, such as covariance and power spectrum, even in the absence of sparsity priors. The framework described here leverages the statistical structure of random processes to enable signal compression and offers an alternative perspective at sparsity-agnostic inference. Capitalizing on parsimonious representations, we illustrate how compression and reconstruction tasks can be addressed in popular applications such as power spectrum estimation, incoherent imaging, direction of arrival estimation, frequency estimation, and wideband spectrum sensing.
Keywords: compass; compressed sensing