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: In this paper, the authors proposed to combine the hypothesis tests in the Haar domain with the decimated biorthogonal Haar transform instead of the classical Haar, which is normalized such that the p -values of Bi-Haar coefficients (p B H ) provide good approximation to those of Haar (p H ) for high-intensity settings or large scales.
30 citations
Dissertation•
21 Aug 2003
TL;DR: It is demonstrated that biorthogonal and orthogonal wavelets generate similar compression performance when they have similar filter properties and both employ symmetric extension, and that linear (or near-linear) phase filters are critical to compression performance—an issue that has not been recognized to date.
Abstract: Effective image compression requires a non-expansive discrete wavelet transform (DWT) be employed; consequently, image border extension is a critical issue. Ideally, the image border extension method should not introduce distortion under compression. It has been shown in literature that symmetric extension performs better than periodic extension. However, the non-expansive, symmetric extension using fast Fourier transform and circular convolution DWT methods require symmetric filters. This precludes orthogonal wavelets for image compression since they cannot simultaneously possess the desirable properties of orthogonality and symmetry. Thus, biorthogonal wavelets have been the de facto standard for image compression applications. The viability of symmetric extension with biorthogonal wavelets is the primary reason cited for their superior performance. Recent matrix-based techniques for computing a non-expansive DWT have suggested the possibility of implementing symmetric extension with orthogonal wavelets. For the first time, this thesis analyzes and compares orthogonal and biorthogonal wavelets with symmetric extension. Our results indicate a significant performance improvement for orthogonal wavelets when they employ symmetric extension. Furthermore, our analysis also identifies that linear (or near-linear) phase filters are critical to compression performance—an issue that has not been recognized to date. We also demonstrate that biorthogonal and orthogonal wavelets generate similar compression performance when they have similar filter properties and both employ symmetric extension. The biorthogonal wavelets indicate a slight performance advantage for low frequency images ; however, this advantage is significantly smaller than recently published results and is explained in terms of wavelet properties not previously considered. Acknowledgments I express my sincere gratitude to my advisor Dr. Amy Bell for her technical and financial support which made this thesis possible. Her constant encouragement, suggestions and ideas have been invaluable to this work. I immensely appreciate the time she devoted reviewing my writing and vastly improving my technical writing skills. Her thoroughness, discipline and work ethic are laudable and worthy of emulation. I would like to thank Dr. Brian Woerner and Dr. Lynn Abbott for reviewing my work and agreeing to serve on my committee. I am also grateful to Dr. Karen Duca in VBI for her financial support and the opportunity to work on some interesting biomedical signal processing problems. I am thankful to my fellow DSPCL colleagues Kishore Kotteri and Krishnaraj Varma for their technical help and insightful suggestions that went a long way in shaping this thesis. My interactions with them greatly improved my technical knowledge and research skills. I am also …
30 citations
TL;DR: In this paper, a new construction of biorthogonal splines for isogeometric mortar methods is proposed, which has local support and optimal approximation properties, which yield optimal results with mortar methods.
29 citations
TL;DR: In this article, an infinite dimensional analysis with respect to non-Gaussian measures of Mittag-Leffler type is presented, where the authors show that the well-known Wick-ordered polynomials in Gaussian analysis cannot be generalized to this nonGaussian case.
29 citations
TL;DR: A formulation of the multiresolution time-domain (MRTD) algorithm using scaling and one-level wavelet basis functions, for orthonormal Daubechies and biorthogonal Cohen-Daubechie-Feauveau (CDF) wavelet families, and the issue of the analytic calculation of the MRTD coefficients is addressed.
Abstract: We present a formulation of the multiresolution time-domain (MRTD) algorithm using scaling and one-level wavelet basis functions, for orthonormal Daubechies and biorthogonal Cohen-Daubechies-Feauveau (CDF) wavelet families. We address the issue of the analytic calculation of the MRTD coefficients. This allows us to point out the similarities and the differences between the MRTD schemes based on the aforementioned wavelet systems and to compare their performances in terms of dispersion error and computational efficiency. The remainder of the paper is dedicated to the implementation of the CDF-MRTD method for scattering problems. We discuss the approximations made in implementing material inhomogeneities and validate the method by numerical examples.
29 citations