Wavelet Based Speech Coding Using Orthogonal Matching Pursuit

A novel waveform approximation called Orthogonal Matching Pursuit 1] (OMP) has been exploited to represent a speech waveform with a set of complex coeecients. The OMP algorithm proved to be quite eeective in approximating waveforms that have their energy concentrated in a short ranges of frequency. The spectrum of speech signals is usually well-localized in frequency and therefore OMP is a suitable tool for the purpose of speech coding. The algorithm has been applied to a standard test signal. Speech coding methods can be categorized into two major groups: those based on reconstructing the speech wave-form (waveform coders), and those that build a speech production model to reproduce the speech (voice coders or vocoders). Waveform coders, themselves, can be divided into two groups: (i) time{domain waveform and (ii) spectral{domain waveform coders. The former takes advantage of the fact that speech is a semi periodic signal meaning that it is periodic over short time intervals, whereas the latter uses the localized properties of the speech signal in frequency domain to code the waveform. In the conventional waveform coding schemes a unitary and linear transform is being used to convert a vector of source samples into another vector, often called transform coeecients, and the corresponding coeecients are quan-tized subsequently. Almost all of the transform coding schemes try to achieve a perfect reconstruction (disregarding the quantization error). Considering the fact that the coeecients representing the waveform have to be quantized prior to transmission and that by nature, the quantiza-tion is a lossy operation, it seems reasonable to relinquish perfect reconstruction in the transformation phase in exchange for further compression. In other words, since the quantization will distort the reconstructed speech wave-form, there is no reason to insist on a set of coeecients that leads to a perfect reconstruction of the original speech waveform. In a recent paper, Vetterli and Kalker 6] proposed a motion compensated video coding based on matching pursuit. In their method, at each iteration a vector is picked from the dictionary such that optimizes the rate{distortion function. The organization of the paper is as follows: Section II describes the overall proposed method including a brief review of the OMP algorithm. Section III, describes the quantizer operation and, nally, Section IV includes some of the results obtained by applying the method to a standard test signal. As with most of the existing speech coding algorithms, the procedure starts with splitting the …