We derived the first sparse recovery guarantees for weighted l1 minimization with sparse random matrices and the class of weighted sparse signals, using a weighted versions of the null space property to derive these guarantees. These sparse matrices from expender graphs can be applied very fast and have other better computational complexities than their dense counterparts. In addition we show t...

In the last decade a broad literature has arisen studying sparse recovery, the estimation of sparse vectors from low dimensional linear projections. Sparse recovery has a wide variety of applications such as streaming algorithms, image acquisition, and disease testing. A particularly important subclass of sparse recovery is the sparse Fourier transform, which considers the computation of a disc...

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 ...

Sparse signal recovery using sparse random projections

Over the recent years, a new *linear* method for compressing high-dimensional data (e.g., images) has been discovered. For any high-dimensional vector x, its *sketch* is equal to Ax, where A is an m x n matrix (possibly chosen at random). Although typically the sketch length m is much smaller than the number of dimensions n, the sketch contains enough information to recover an *approximation* t...