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
More filters
TL;DR: The collocation method proposed by Cai and Wang1 has been reviewed in detail to solve singularly perturbed reaction diffusion equation of elliptic and parabolic types based on an interpolating wavelet transform using cubic spline on dyadic points.
Abstract: In this paper, the collocation method proposed by Cai and Wang1 has been reviewed in detail to solve singularly perturbed reaction diffusion equation of elliptic and parabolic types. The method is based on an interpolating wavelet transform using cubic spline on dyadic points. Adaptive feature is performed automatically by thresholding the wavelet coefficients. Numerical examples are presented for elliptic and parabolic problems. The purposed method comes up as a powerful tool for studying singular perturbation problems in term of effective grid generation and CPU time.
24 citations
01 Jan 2014
TL;DR: In this paper, it was shown that for many practical purposes of signal processing, a tight frame is almost as good as an orthonormal basis for data compression, which is performed by removing all wavelet expansion coefficients below a fixed threshhold.
Abstract: As we have seen in Section 12.5, the discretization of the CWT leads, among other things, to the theory of frames. For many practical purposes of signal processing, a tight frame is almost as good as an orthonormal basis. Actually, if one stays with the standard wavelets, as we have done so far, one cannot do better, since these wavelets do not generate any orthonormal basis (like the usual coherent states). There are cases, however, in which an orthonormal basis is really required. A typical example is data compression, which is performed (in the simplest case) by removing all wavelet expansion coefficients below a fixed threshhold. In order to not introduce any bias in this operation, the coefficients have to be as decorrelated as possible, and, of course, an orthonormal basis is ideal in this respect.
24 citations
TL;DR: This paper describes an efficient approach to the fusion of spatially registered images and image sequences that uses an improved wavelet representation, which has low redundancy as well as near-shift-invariance and corresponds to an optimal strategy.
Abstract: This paper describes an efficient approach to the fusion of spatially registered images and image sequences. The fusion method uses an improved wavelet representation, which has low redundancy as well as near-shift-invariance. Specifically, this representation is derived from an extended discrete wavelet frame with variable resampling strategies, and it corresponds to an optimal strategy. The proposed method lends itself well to rapid fusion for image sequences. Experimental results tested on different types of imagery show that the proposed method, as a shift-invariant scheme, provides better results than conventional wavelet methods and it is much more efficient than existing shift-invariant methods (the undecimated wavelet and the dual-tree complex wavelet methods).
24 citations
TL;DR: A sparse approximation scheme inspired from the functional architecture of the primary visual cortex is implemented, which models simple and complex cell receptive fields through log-Gabor wavelets and incorporates inhibition and facilitation interactions between neighboring cells.
Abstract: Several drawbacks of critically sampled wavelets can be solved by overcomplete multiresolution transforms and sparse approximation algorithms. Facing the difficulty to optimize such nonorthogonal and nonlinear transforms, we implement a sparse approximation scheme inspired from the functional architecture of the primary visual cortex. The scheme models simple and complex cell receptive fields through log-Gabor wavelets. The model also incorporates inhibition and facilitation interactions between neighboring cells. Functionally these interactions allow to extract edges and ridges, providing an edge-based approximation of the visual information. The edge coefficients are shown sufficient for closely reconstructing the images, while contour representations by means of chains of edges reduce the information redundancy for approaching image compression. Additionally, the ability to segregate the edges from the noise is employed for image restoration.
24 citations
TL;DR: The use of orthogonal wavelet transforms in preprocessing multivariate data for subsequent analysis, e.g., by clustering the dimensionality reduction, is discussed.
Abstract: We discuss the use of orthogonal wavelet transforms in preprocessing multivariate data for subsequent analysis, e.g., by clustering the dimensionality reduction. Wavelet transforms allow us to introduce multiresolution approximation, and multiscale nonparametric regression or smoothing, in a natural and integrated way into the data analysis. As will be explained in the first part of the paper, this approach is of greatest interest for multivariate data analysis when we use (i) datasets with ordered variables, e.g., time series, and (ii) object dimensionalities which are not too small, e.g., 16 and upwards. In the second part of the paper, a different type of wavelet decomposition is used. Applications illustrate the powerfulness of this new perspective on data analysis.
23 citations