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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TL;DR: In this paper, it was shown that for any expansive matrix A with integer entries, there exist a -dilation FMRA orthogonal wavelet with non-integer entries.
Abstract: A frame multiresolution (FMRA for short) orthogonal
wavelet is a single-function orthogonal wavelet such that the
associated scaling space V
0 admits a normalized tight frame
(under translations). In this article, we prove that for any
expansive matrix A with integer entries, there exist
A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets
for some other expansive matrix with non integer entries are also discussed.
20 citations
TL;DR: The wavelet-Galerkin approach allows the transient flow equations to be solved directly for the expansion coefficients at a certain level of resolution, which can be used to form the wavelet multiresolution framework that can be utilized for further analysis, such as feature extraction and signal identification.
Abstract: In this paper, a wavelet-Galerkin method is utilized to solve the hyperbolic partial differential equations describing transient flow in a simple pipeline. Two wavelets (Haar and Daubechies) are utilized as bases for the Galerkin scheme. The governing equations are solved for the expansion coefficients, which are then used to reconstruct the signal at the downstream end of the pipeline; the computed results are in an excellent agreement with those calculated by using the method of characteristics including laminar or linearized turbulent friction terms. Most importantly, the wavelet-Galerkin approach allows the transient flow equations to be solved directly for the expansion coefficients at a certain level of resolution. This can be used to form the wavelet multiresolution framework that can be utilized for further analysis, such as feature extraction and signal identification.
20 citations
23 Aug 2004
TL;DR: A multiscale algorithm for matching and classifying 2-D shapes is developed that is invariant to the affine transformation and to the boundary starting point variation and is not sensitive to small boundary deformations.
Abstract: A multiscale algorithm for matching and classifying 2-D shapes is developed. The algorithm uses the 1-D dyadic wavelet transform (DWT) to decompose a shape's boundary into multiscale levels. Then the coarse to fine matching and classification are achieved in two stages. In the first stage, the global features are extracted by calculating the curve moment invariants of the approximation coefficients. By calculating the normalized cross correlation of the 1-D triangle area representation of the detail coefficients, the local similarity is achieved by the second stage. The proposed algorithm is invariant to the affine transformation and to the boundary starting point variation. In addition, the results demonstrate that the new algorithm is not sensitive to small boundary deformations.
20 citations
01 Jan 2000
TL;DR: In this paper, a contrast based multiresolution image fusion technique is proposed, in which the input multispectral images are decomposed by wavelet transform, while the multireolution contrast sequences of each input image can be obtained.
Abstract: This paper introduces a contrast based multiresolution image fusion technique.Three steps can implement the method: First,the input multispectral images are decomposed by wavelet transform,meanwhile,the multiresolution contrast sequences of each input images can be obtained.Second,according to the contrast based criterion,the multiresolution analysis of the fused image can be obtained on the corresponding levels of the multiresolution analysis of the input images.Finally,the output image can be obtained through inverse wavelet transform.This algorithm is tested by fusing the visual and infrared images from same scence.The experiment shows that the fused image can preserve the details of the each input images successfully.
20 citations
01 Dec 2013
TL;DR: The method detects intervals where time series features differ from their surroundings, and it produces a multiresolution analysis of the series as a sum of scale-dependent components obtained from differences of smooths.
Abstract: A scale space multiresolution feature extraction method is proposed for time series data The method detects intervals where time series features differ from their surroundings, and it produces a multiresolution analysis of the series as a sum of scale-dependent components These components are obtained from differences of smooths The relevant sequence of smoothing levels is determined using derivatives of smooths with respect to the logarithm of the smoothing parameter As time series are usually noisy, the method uses Bayesian inference to establish the credibility of the components © The Authors Stat published by John Wiley & Sons Ltd
20 citations