title: A simple method to build oversampled filter banks and tight frames.
abstract: 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.
authors.affiliation: Institute of Aerospace Science and Technology, Shanghai Jiaotong University, Shanghai 20030, China. yangbo_sd@sjtu.edu.cn
authors.forename: Bo
authors.initials: B
authors.lastname: Yang
authors.forename: Zhongliang
authors.initials: Z
authors.lastname: Jing
mesh_terms: 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