Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.

Construction of Arbitrary Dimensional Biorthogonal Multiwavelet Using Lifting Scheme

Abstract: This paper focuses on the construction of multidimensional biorthogonal multiwavelets and the perfect reconstruction multifilter banks. Based on the Hermite-Neville filter, two lifting structures have been proposed and systematically investigated, and a general design framework has been developed for building biorthogonal multiwavelets and Hermite interpolation filter banks with any multiplicity for any lattice in any dimension with any number of primal and dual vanishing moments. The construction is an important generalization of the Neville-based lifting scheme and inherits all of the advantages of lifting schemes such as fast transform, in-place computation and integer-to-integer transforms. Our multi wavelet systems preserve most of the desirable properties for applications, such as interpolating, short support, symmetry, and high vanishing moments.

Biorthogonal bases of symmetric compactly supported wavelets

Abstract: Note: M. Farges et al, Eds. Reference LCAV-CHAPTER-2005-011 Record created on 2005-06-27, modified on 2017-05-12

Theory and design of arbitrary-length biorthogonal cosine-modulated filter banks

Abstract: The design and generalization of Perfect-Reconstruction (PR) cosine-modulated filter banks (CMFB) have been studied extensively due to its low design and implementation complexity. In this paper, the theory and design of arbitrary-length biorthogonal CMFB is considered. This is a generalization of the method for designing arbitrary length orthogonal CMFB and has the advantage of simple design procedure. We also propose a systematic design method so that biorthogonal CMFB with longer length can be obtained.

New class of wavelets for signal approximation

Abstract: This paper develops a new class of wavelets for which the classical Daubechies zero moment property has been relaxed. The advantages of relaxing higher order wavelet moment constraints is that within the framework of compact support and perfect reconstruction (orthogonal and biorthogonal) one can obtain wavelet basis with new and interesting approximation properties. This paper investigates a new class of wavelets that is obtained by setting a few lower order moments to zero and using the remaining degrees of freedom to minimize a larger number of higher order moments. The resulting wavelets are shown to be robust for representing a large classes of inputs. Robustness is achieved at the cost of exact representation of low order polynomials but with the advantage that higher order polynomials can be represented with less error compared to the maximally regular solution of the same support.