A Reed-Solomon Code Based Measurement Matrix with Small Coherence

In this letter, we construct a class of deterministic measurement matrices which are asymptotically optimal. For this purpose, we first apply the tensor product over the Reed Solomon (R-S) generator matrix to produce a new one; then employing this generator matrix, we construct a measurement matrix. If the R-S code is defined on \BBFq, then the resulting measurement matrices are of dimensions q
²
×q
³
, where q is an arbitrary prime power and its coherence would be
¹
/q, which is desirable for compressive sampling. We also illustrate the effectiveness of our proposed matrices in compressed sensing with some simulation examples.