Multidimensional Perfect Reconstruction Filter Banks Research Articles

Image Fusion Algorithm Based on the Quincunx-sampled Discrete Wavelet Frame

A novel image fusion algorithm based on the quincunx-sampled discrete wavelet frame is presented.Firstly, the replaceability of sampling matrix for multidimensional perfect reconstruction filter banks is shown;based on this, the quincunx-sampled discrete wavelet frame is derived, and its characteristics are discussed.Then, the frame is incorporated into the multiscale-based image fusion scheme, and a nearly shift-invariant fusion algorithm with low redundancy is obtained.Finally, the algorithm is tested and compared with existing algorithms.The results show that the algorithm can produce high-quality fused images rapidly.

Multidimensional perfect reconstruction filter banks: an approach of algebraic geometry

In image compression and some other applications, multidimensional filter banks are gaining their popularity due to the decrease in implementation cost. In this article, we study these filter banks from a viewpoint of algebraic geometry, where some insights are emerging. Familiar properties, such as perfect reconstruction and linear phase, appear differently when studied from this new angle. For the sake of practicability and a better understanding of problems, our focus in this work is further restricted to the filter banks that can achieve linear phase and perfect reconstruction properties. According to different symmetry nature, the filter banks are categorized into two types. Filters in a multidimensional filter bank represented by multivariate polynomials have common zeros that are different in nature from their 1D counterparts. In this work, the relation between the above-mentioned properties and various zeros is investigated. A criterion to test such filter banks is proposed and this criterion is also interpreted in resultant theory. Based on these results, as well as a proposed conjecture, a factorization of lifting scheme is presented for one type of these filter banks. For the other type of filter banks, we propose a method on perfect reconstruction completion.

Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for R/sup n/

New results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented. Among the topics discussed are sampling in multiple dimensions, multidimensional perfect reconstruction filter banks, the two-channel case in multiple dimensions, the synthesis of multidimensional filter banks, and the design of compactly supported wavelets. >