Signal compression using redundant 1-D discrete wavelet transforms

Methods of compressing data prior to storage and/or transmission are of significant practical and commercial interest. Signal compression using wavelet expansion-based transform coding techniques has become popular. In addition to providing maximum compression, signal compression algorithms should be designed to provide good signal reconstruction with minimum computational overhead. To facilitate compression and storage, the sub-band coefficients are quantized. The quantization process is irreversible and introduces distortion. The Discrete Wavelet Transform (DWT) filter bank perfect reconstruction property no longer holds. Further, aliasing of quantization error leads to large distortion in the reconstructed signal.

The concept of the Overcomplete Discrete Wavelet Transform (ODWT) is introduced. The general idea is to exploit the phase shift relationship between ODWT quantized member sets and develop an iterative process wherein one ODWT quantized member set is used to improve the quality of the other. This idea has been implemented with Haar wavelets and Daubechies DB2 wavelets. The results are used to explore the feasibility of adding this ODWT functionality to existing signal compression algorithms like SPIHT, which uses the Daubechies 9, 7 biorthogonal wavelet.