Sparse Recovery with Very Sparse Compressed Counting

Compressed1 sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently [11] developed the methodology of using (dense) Compressed Counting for recovering nonnegative Ksparse signals. In this paper, we adopt very sparse Compressed Counting for nonnegative signal recovery. Our design matrix is sampled from a maximally-skewed α-stable distribution (0 < α < 1), and we sparsify the design matrix so that on average (1−γ)-fraction of the entries become zero. The idea is related to very sparse stable random projections [9, 6], the prior work for estimating summary statistics of the data.