A simple method to build oversampled filter banks and tight frames.
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 oversampled 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.
Yang
Bo
B
Institute of Aerospace Science and Technology, Shanghai Jiaotong University, Shanghai 20030, China. yangbo_sd@sjtu.edu.cn
Jing
Zhongliang
Z
D000465:Algorithms; D017076:Computer-Aided Design; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D012984:Software; D012985:Software Design