Discrete Cosine Wavelet Packet Transform and Its Application in Compressed Sensing for Speech Signal

This paper concerns the compressed sensing of speech signal. Discrete cosine wavelet packet transform (DCWPT) is proposed for speech signal based on the properties of discrete cosine transform (DCT) and wavelet packet transform (WPT). Coefficients of DCWPT can be obtained by WPT from the DCT coefficients, and speech signals are sparser in DCWPT domain than in DCT domain. In order to apply this newly efficient transform into the compressed sensing for speech signal successfully, the sparse decomposition matrix of DCWPT is constructed at first. The orthogonal matching pursuit reconstruction algorithm has also be optimized according to the sparse decomposition matrix and psycho-acoustics, and a new framework of the compressed sensing for speech signal based on DCWPT is established. The conclusion that the new method is better than the traditional DCT method is made from experiment by subjective and objective indicators.