Deterministic compressed-sensing matrix from grassmannian matrix: Application to speech processing

Abstract

Reconstruction of a signal based on Compressed Sensing (CS) framework relies on the knowledge of the sparse basis & measurement matrix used for sensing. While most of the studies so far focus on the prominent random Gaussian, Bernoulli or Fourier matrices, we have proposed construction of efficient sensing matrix we call Grassgram Matrix using Grassmannian matrices. This work shows how to construct effective deterministic sensing matrices for any known sparse basis which can fulfill incoherence or RIP conditions with high probability. The performance of proposed approach is evaluated for speech signals. Our results shows that these deterministic matrices out performs other popular matrices.