Additive character sequences with small alphabets for compressed sensing matrices

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a K × N measurement matrix for compressed sensing is deterministically constructed via additive character sequences. The Weil bound is then used to show that the matrix has asymptotically optimal coherence for N = K², and that it is a tight frame. A sparse recovery guarantee for the incoherent tight frame is also discussed. Numerical results show that the deterministic sensing matrix guarantees empirically reliable recovery performance via an l₁-minimization method for noiseless measurements.