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A Simple Method to Build Oversampled Filter Banks and Tight Frames

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2 Author(s)
Bo Yang ; Shanghai Jiaotong Univ., Shanghai ; Zhongliang Jing

This paper presents conditions under which the sampling lattice for a filter bank can be replaced without loss of perfect reconstruction. This is the generalization of common knowledge that removing up/downsampling will not lose perfect reconstruction. The results provide a simple way of building over- sampled filter banks. If the original filter banks are orthogonal, these oversampled banks construct tight frames of l2(Z n) when iterated. As an example, a quincunx lattice is used to replace the rectangular one of the standard wavelet transform. This replacement leads to a tight frame that has a higher sampling in both time and frequency. The frame transform is nearly shift invariant and has intermediate scales. An application of the transform to image fusion is also presented.

Published in:

Image Processing, IEEE Transactions on  (Volume:16 ,  Issue: 11 )