Efficient dyadic wavelet transformation of images using interpolation filters

Authors:
Michael Unser
Affiliations:
Biomedical Engineering and Instrumentation Program, NCRR, National Institutes of Health, Bethesda, MD
Venue:
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: image and multidimensional signal processing - Volume V
Year:
1993

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Abstract

The properties of a special class of overcomplete wavelet transforms specified in terms of an interpolation filter are investigated. The decomposition is obtained by filtering the signal with a sequence of increasingly selective lowpass filters with a dyadic scale progression. The wavelet coefficients are evaluated by simple subtraction of two consecutive lowpass components. The lowpass filter bank is implemented using a standard iterative multiscale algorithm. The impulse responses of the analysis filters are shown to be interpolated versions of each other. This structure is computationally very efficient; it requires a little more than 1/4 as many operations as other comparable wavelet-based algorithms. The corresponding filter bank provides a perfect coverage of the frequency domain which results in a trivial reconstruction procedure by summation. Extensions for the sub-sampled case are also presented. The decompositions associated with spline interpolation filters are considered in more details and some image processing examples are presented.