On Sparse Compression Complexity of Speech Signals

Abstract

In this paper, we have addressed the issue of the sparse compression complexity for the speech signals. First of all, this work illustrated the effect of the signal length on the complexity levels of Matching Pursuit (MP) and Orthogonal Matching Pursuit (OMP) algorithms. Also, this paper introduced a study of possibility to reduce that complexity by exploiting the shared atoms among the contiguous speech compressions. By comparing the shared atoms levels and a threshold level induced by an analytic model based on the both the central and non-central hyper-geometric distributions, we proved the ability of the shared atoms criterion to detect if there is biasing towards a subspace of atoms or not, and to decide if the biasing occurs due to the redundancy in the dictionary of atoms, or due to the redundancy in the signal itself.
Moreover, we suggested a subspace bias-based approaches for complexity reduction called "Atoms Reuse" and "Active Cluster". Both methods exploits the higher levels of the shared atoms to reduce the compression complexity by reducing the search space during the pursuit iterations.