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.
Papers published on a yearly basis
Papers
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TL;DR: An optimal P-band perfect reconstruction filter bank (PRFB) is derived in this paper, which minimizes the approximation error (in the mean-square sense) between the original signal and its low-resolution version.
Abstract: An important issue in multiresolution analysis is that of optimal basis selection. An optimal P-band perfect reconstruction filter bank (PRFB) is derived in this paper, which minimizes the approximation error (in the mean-square sense) between the original signal and its low-resolution version. The resulting PRFB decomposes the input signal into uncorrelated, low-resolution principal components with decreasing variance. Optimality issues are further analyzed in the special case of stationary and cyclostationary processes. By exploiting the connection between discrete-time filter banks and continuous wavelets, an optimal multiresolution decomposition of L/sub 2/(R) is obtained. Analogous results are also derived for deterministic signals. Some illustrative examples and simulations are presented. >
194 citations
01 Aug 1996
TL;DR: This work shows how to perform multiresolution analysis of colored meshes by separately analyzing shape and color and describes efficient algorithms and data structures that allow us to incrementally construct lower resolution approximations to colored meshes from the geometry and color wavelet coefficients at interactive rates.
Abstract: Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and level-of-detail control of complex meshes in a unified and theoretically sound way. We extend previous work on multiresolution analysis of meshes in two ways. First, we show how to perform multiresolution analysis of colored meshes by separately analyzing shape and color. Second, we describe efficient algorithms and data structures that allow us to incrementally construct lower resolution approximations to colored meshes from the geometry and color wavelet coefficients at interactive rates. We have integrated these algorithms in a prototype mesh viewer that supports progressive transmission, dynamic display at a constant frame rate independent of machine characteristics and load, and interactive choice of tradeoff between the amount of detail in geometry and color. The viewer operates as a helper application to Netscape, and can therefore be used to rapidly browse and display complex geometric models stored on the World Wide Web. CR
193 citations
TL;DR: It is shown that, although these stiffness matrices are generally not sparse, the order of the overall computational work which is needed to realize a certain accuracy is of the formO(N(logN)b), whereN is the number of unknowns andb ≥ 0 is some real number.
Abstract: This is the second part of two papers which are concerned with generalized Petrov-Galerkin schemes for elliptic periodic pseudodifferential equations in ℝ
n
. This setting covers classical Galerkin methods, collocation, and quasi-interpolation. The numerical methods are based on a general framework of multiresolution analysis, i.e. of sequences of nested spaces which are generated by refinable functions. In this part, we analyse compression techniques for the resulting stiffness matrices relative to wavelet-type bases. We will show that, although these stiffness matrices are generally not sparse, the order of the overall computational work which is needed to realize a certain accuracy is of the formO(N(logN)
b
), whereN is the number of unknowns andb ≥ 0 is some real number.
190 citations
TL;DR: A generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors and it is proved that these functions are square-integrable and that they converge to their classical counterparts of the corresponding order.
Abstract: We present a generalization of the orthonormal Daubechies wavelets and of their related biorthogonal flavors (Cohen-Daubechies-Feauveau, 9/7). Our fundamental constraint is that the scaling functions should reproduce a predefined set of exponential polynomials. This allows one to tune the corresponding wavelet transform to a specific class of signals, thereby ensuring good approximation and sparsity properties. The main difference with the classical construction of Daubechies is that the multiresolution spaces are derived from scale-dependent generating functions. However, from an algorithmic standpoint, Mallat's fast wavelet transform algorithm can still be applied; the only adaptation consists in using scale-dependent filter banks. Finite support ensures the same computational efficiency as in the classical case. We characterize the scaling and wavelet filters, construct them and show several examples of the associated functions. We prove that these functions are square-integrable and that they converge to their classical counterparts of the corresponding order.
189 citations
TL;DR: To overcome the limitation of the Fourier transform, the Gabor wavelet is introduced to analyze the phase distributions of the spatial carrier-fringe pattern and the theory of wavelet transform profilometry is presented.
Abstract: We present an analysis of a spatial carrier-fringe pattern in three-dimensional (3-D) shape measurement by using the wavelet transform, a tool excelling for its multiresolution in the time- and space-frequency domains. To overcome the limitation of the Fourier transform, we introduce the Gabor wavelet to analyze the phase distributions of the spatial carrier-fringe pattern. The theory of wavelet transform profilometry, an accuracy check by means of a simulation, and an example of 3-D shape measurement are shown.
188 citations