Combining the discrete wavelet transform and mixed-domain filtering

A novel filtering method is proposed that combines the discrete orthogonal wavelet transform (DWT) with the mixeddomain (mixed-D) filtering method. The method uses the DWT to pre- and postprocess those dimensions of the signal that are transformed to the discrete-frequency domain by mixed-D filtering. Using the DWT in this manner provides a controlled mechanism to partition the spectrum of the input signal into subband signals, which then may be selectively filtered during the linear difference equation (LDE) step of the mixed-D algorithm. It is shown that, when the DWT is computed using filters with ideal high- and lowpass frequency responses, the LDE filters used in the mixed-D filtering stage are unchanged by the introduction of the DWT (although the frequency tuple associated with each LDE filter is altered). This indicates that the mixed-D filtering scheme can be easily used in subband coding systems. Results are given for the filtering of a three-dimensional (3-D) linear trajectory signal, representing a common application in video processing.