Compressive Sampling Patterns for Sparse Recovery via Discrete Cosine Transform Type-I Even

In this work, the problem of recovery of sparse signals by means of compressed sensing in the Discrete Cosine Transform (DCT) domain is addressed. We design a new sampling pattern in the transform domain which is a generalization of arithmetic sequences of difference d. For the DCT Type-I even (DCT1e), we provide a rigorous characterization of the differences
$d$
that ensure perfect recovery of sparse signals from their corresponding arithmetic sampling sequences in the transform domain. They constitute new universal sampling patterns, which guarantee the reconstruction of sparse signals from a minimal amount of measurements in the DCT1e domain. Simulations illustrate the good behavior of traditional compressed sensing solvers with this novel compressive sampling scheme, outperforming the sparse recovery rate of the existing solution for the DCT1e.