A study on the compressibility of speech for compressive speech enhancement

Compressed sensing (CS) based speech enhancement methods are gaining popularity as they do not require any prior information about the noise or a voice activity detector to enhance the noisy observation. CS rests only on the assumption that sparse signals with a small set of observations can be reconstructed with an overwhelming probability. As speech is generally sparse in the time-frequency domain whereas noise is not, CS can be effectively used to reconstruct only the sparse component in the tune-frequency noisy signal, which in tins case is speech. However, one critical issue remains unanswered is the sparsity of the signal in question, i.e., how sparse should speech be assumed? Tins paper studies the effect of the sparsity level in the time-frequency speech representation for use in CS based speech enhancement methods. In an effort to quantify the sparsity of speech, the notion of speech compressibility is used. Specifically, the sparsity of speech and noise in the frequency domain is analyzed by using the power law decay to construct the compressibility level. These findings provide an indicative compressibility theoretical limit on the sparsity assumption in CS speech enhancement or sparse speech reconstruction in general.