Topic
Multiresolution analysis
About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.
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01 Jan 1998
TL;DR: This work describes the full set of Daubechies Wavelets with a particular emphasis on symmetric (and complex) orthonormal bases and describes a multiscale image enhancement algorithm using the phase of the complex multiresolution representation of the 2 dimension signals.
Abstract: The first part of this work describes the full set of Daubechies Wavelets with a particular emphasis on symmetric (and complex) orthonormal bases. Some properties of the associated complex scaling functions are presented in a second part. The third and last part describes a multiscale image enhancement algorithm using the phase of the complex multiresolution representation of the 2 dimension signals.
26 citations
TL;DR: An effective prediction algorithm is described for the next resolution level wavelet coefficients, based on the approximate wave function expanded up to a given level, which results in a reasonable approximation of the wave function and allows to sort out the unnecessary wavelets with a great reliability.
Abstract: The wave function of a many electron system contains inhomogeneously distributed spatial details, which allows to reduce the number of fine detail wavelets in multiresolution analysis approximations. Finding a method for decimating the unnecessary basis functions plays an essential role in avoiding an exponential increase of computational demand in wavelet-based calculations. We describe an effective prediction algorithm for the next resolution level wavelet coefficients, based on the approximate wave function expanded up to a given level. The prediction results in a reasonable approximation of the wave function and allows to sort out the unnecessary wavelets with a great reliability.
26 citations
01 Jan 2004
TL;DR: The numerical examples show that the continuous wavelet transform constructed in this paper has higher computing accuracy compared with the classical continuous wavelets transform.
Abstract: In this paper, we propose a new type of continuous wavelet transform. However we discretize the variables of integral a and b, any numerical integral has a high resolution and a does not appear in the denominator of the integrand. Furthermore, we give two discretization methods of the new wavelet transform. For the one-dimensional situation, we give quadrature formula of the discretized inverse wavelet transform. For the multidimensional situation, we develop the commonly wavelet network based on the discretized inverse wavelet transform of the new wavelet transform. Finally, the numerical examples show that the continuous wavelet transform constructed in this paper has higher computing accuracy compared with the classical continuous wavelet transform.
26 citations
TL;DR: This work proposes a novel multiresolution scheme to generate multiresolving Fourier descriptors: downsampling expansion followed by upsampling reconstruction, which shows that the scheme outperforms both wavelet and traditional Fourier descriptions in terms of accuracy and efficiency.
Abstract: Complex shapes can be effectively analyzed by multiresolution shape descriptors. Compared with wavelet descriptors that are widely used for multiresolution analysis, Fourier descriptors have better invariance properties and higher computational efficiency. We propose a novel multiresolution scheme to generate multiresolution Fourier descriptors for multiresolution analysis: downsampling expansion followed by upsampling reconstruction. Simulation shows that our multiresolution scheme outperforms both wavelet and traditional Fourier descriptors in terms of accuracy and efficiency.
26 citations
24 Oct 1999
TL;DR: Some experimental results on real medical meshes prove the efficiency of the proposed subdivision scheme derived from the regular 1:4 face split, allowing analysis of irregularly subdivided triangular meshes by the wavelet transforms in multiresolution schemes.
Abstract: We propose a new subdivision scheme derived from the regular 1:4 face split, allowing analysis of irregularly subdivided triangular meshes by the wavelet transforms. Some experimental results on real medical meshes prove the efficiency of this approach in multiresolution schemes. In addition we show the effectiveness of the proposed algorithm for lossless compression.
26 citations