Regular Wavelets: A Discrete-Time Approach

Regularity is a new filter property, brought by wavelet theory, for perfect reconstruction octave-band filter banks. Tools for investigating its role in coding applications are provided in this note. First, discrete-time interpretations an optimal estimates of regularity are reviewed. Then, a simple design procedure for paraunitary FIR filter banks with optimal trade-off between frequency selectivity and regularity is given. Finally, the obtained filters are used to measure the effect of regularity versus frequency selectivity in a still image compression scheme with optimized rate-distortion. In this case, regularity is shown to be more relevant than frequency selectivity, especially for short filters.