Topic
Fast wavelet transform
About: Fast wavelet transform is a research topic. Over the lifetime, 2723 publications have been published within this topic receiving 73435 citations.
Papers published on a yearly basis
Papers
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
Abstract: We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.
9,149 citations
TL;DR: In this paper, a lifting scheme is proposed for constructing compactly supported wavelets with compactly support duals, which can also speed up the fast wavelet transform and is shown to be useful in the construction of wavelets using interpolating scaling functions.
2,461 citations
TL;DR: The lifting wavelet as discussed by the authors is a simple construction of second generation wavelets that can be adapted to intervals, domains, surfaces, weights, and irregular samples, and it leads to a faster, in-place calculation of the wavelet transform.
Abstract: We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included.
2,210 citations
TL;DR: A novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph using the spectral decomposition of the discrete graph Laplacian L, based on defining scaling using the graph analogue of the Fourier domain.
2,204 citations
1 Jan 1995
TL;DR: A reconstruction subject to far weaker Gibbs phenomena than thresholding based De-Noising using the traditional orthogonal wavelet transform is produced.
Abstract: De-Noising with the traditional (orthogonal, maximally-decimated) wavelet transform sometimes exhibits visual artifacts; we attribute some of these—for example, Gibbs phenomena in the neighborhood of discontinuities—to the lack of translation invariance of the wavelet basis. One method to suppress such artifacts, termed “cycle spinning” by Coifman, is to “average out” the translation dependence. For a range of shifts, one shifts the data (right or left as the case may be), De-Noises the shifted data, and then unshifts the de-noised data. Doing this for each of a range of shifts, and averaging the several results so obtained, produces a reconstruction subject to far weaker Gibbs phenomena than thresholding based De-Noising using the traditional orthogonal wavelet transform.
2,197 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2023 | 4 |
| 2022 | 6 |
| 2021 | 3 |
| 2020 | 7 |
| 2019 | 1 |