Topic
Biorthogonal system
About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.
Papers published on a yearly basis
Papers
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TL;DR: Regular biorthogonal linear-phase filter banks are designed according to the proposed theory and are found to provide better objective performance and improved perceptual quality of the decompressed images.
Abstract: Regularity is a fundamental and desirable property of wavelets and perfect reconstruction filter banks (PRFBs). Among others, it dictates the smoothness of the wavelet basis and the rate of decay of the wavelet coefficients. This paper considers how regularity of a desired degree can be structurally imposed onto biorthogonal filter banks (BOFBs) so that they can be designed with exact regularity and fast convergence via unconstrained optimization. The considered design space is a useful class of M-channel causal finite-impulse response (FIR) BOFBs (having anticausal FIR inverses) that are characterized by the dyadic-based structure W(z)=I-UV/sup /spl dagger//+z/sup -1/UV/sup /spl dagger// for which U and V are M/spl times//spl gamma/ parameter matrices satisfying V/sup /spl dagger//U=I/sub /spl gamma//, 1/spl les//spl gamma//spl les/M, for any M/spl ges/2. Structural conditions for regularity are derived, where the Householder transform is found convenient. As a special case, a class of regular linear-phase BOFBs is considered by further imposing linear phase (LP) on the dyadic-based structure. In this way, an alternative and simplified parameterization of the biorthogonal linear-phase filter banks (GLBTs) is obtained, and the general theory of structural regularity is shown to simplify significantly. Regular BOFBs are designed according to the proposed theory and are evaluated using a transform-based image codec. They are found to provide better objective performance and improved perceptual quality of the decompressed images. Specifically, the blocking artifacts are reduced, and texture details are better preserved. For fingerprint images, the proposed biorthogonal transform codec outperforms the FBI scheme by 1-1.6 dB in PSNR.
30 citations
TL;DR: The proposed scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature or cascade or parallel implementation.
30 citations
TL;DR: In this paper, the Riesz wavelet associated with multiresolution analyses (MRAs) was characterized and the dual of the wavelet was shown to have a dual Riestz wavelet.
30 citations
01 Jan 2005
TL;DR: In this paper, the definition of multivariate biorthogonal multi-wavelet packets associated with multiple scaling functions in higher dimension is given and an algorithm for constructing them is proposed.
Abstract: In this paper,the definition for the multivariate biorthogonal multiwavelet packets associated with multiple scaling functions in higher dimension is given and an algorithm for constructing them is proposed.The biorthogonality property for multivariate biorthogonal multiwavelet packets has been studied.
30 citations
TL;DR: In this paper, the authors constructed biorthogonal spline wavelets on the interval for different spline orders and used them for the resolution of elliptic boundary problems both with pure Galerkin and Petrov-Galerkin schemes.
Abstract: We construct biorthogonal spline wavelets on the interval for different spline orders. We then discuss the accuracy of the construction and test the wavelet transform. Building the corresponding wavelet basis for boundary conditions we use it for the resolution of elliptic boundary problems both with pure Galerkin and Petrov-Galerkin schemes. The results are compared from stability and convergence points of view. The main conclusion is that using the biorthogonal counterpart of spline functions as trial spaces for low order splines provides much more advantages than using spline functions themselves as trial spaces for high order splines.
30 citations