An M-band, 2-dimensional translation-invariant wavelet transform and applications

This paper develops a two-dimensional M-band translation-invariant wavelet transform (2-D MTI). Use of the MTI overcomes the shift-variance of the wavelet transform by applying a cost function over M shifts of the input signal. The new transform is proven to be translation-invariant. Use of M-band wavelets enables a finer frequency partitioning and greater energy compaction in the transform representation. Examples are presented which show that the translation-invariant transforms provide superior energy concentration compared to the corresponding nominal wavelet transforms. Examples are also presented comparing the energy concentration capability of M-band wavelets and the modulated lapped transform (MLT). We explored the MTI as a tool for image processing by using it to represent several different images.