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.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Nam Yul Yu
• Keywords: Deterministic Sensing Matrix, ICASSP 2011, Sensing, Signal Processing, Tight Frame