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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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Journal ArticleDOI
TL;DR: A system is proposed for texture analysis and classification of lesions in mammographic images and the performance of the polynomial classifier has proved to be better in comparison to other classification algorithms.
Abstract: Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98+/-0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms.

74 citations

Journal ArticleDOI
TL;DR: The MADNESS (multiresolution adaptive numerical environment for scientific simulation) as mentioned in this paper is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision that are based on multiresolution analysis and separated representations.
Abstract: MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision that are based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics.

74 citations

01 Jan 2001
TL;DR: It is shown that by analyzing the resulting transient information only, current onset detection algorithms can be improved considerably, especially for those instruments with noisy attack information, such as plucked or struck strings.
Abstract: Whilst musical transients are generally acknowledged as holding much of the perceptual information within musical tones, most research in sound analysis and synthesis tends to focus on the steady state components of signals. A method is presented which separates the noisy transient information from the slowly time varying steady state components of musical audio. Improvements of using adaptive thresholding, and multiresolution analysis methods are then illustrated. It is shown that by analyzing the resulting transient information only, current onset detection algorithms can be improved considerably, especially for those instruments with noisy attack information, such as plucked or struck strings. The idea is then applied to audio processing techniques to enhance or decrease the strength of note attack information. Finally, the transient extraction algorithm (TSS) is applied to time-scaling implementation, where the transient and noise information is analyzed so that only steady state regions are stretched, yielding considerably improved results.

74 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that for every expanding integer matrix A ∈ Mn(ℤ) there is a Haar type orthonormal wavelet basis having dilation factor A and translation lattice ℤn.
Abstract: K.-H. Grochenig and A. Haas asked whether for every expanding integer matrix A ∈ Mn(ℤ) there is a Haar type orthonormal wavelet basis having dilation factor A and translation lattice ℤn. They proved that this is the case when the dimension n = 1. This article shows that this is also the case when the dimension n = 2.

73 citations

Journal ArticleDOI
TL;DR: This review paper is intended to give a useful guide for those who want to apply the discrete wavelet transform in practice, and discusses practical applications of the wavelet machinery.
Abstract: This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous proofs of mathematical statements are omitted, and the reader is just referred to corresponding literature. The multiresolution analysis and fast wavelet transform became a standard procedure for dealing with discrete wavelets. The proper choice of a wavelet and use of nonstandard matrix multiplication are often crucial for achievement of a goal. Analysis of various functions with the help of wavelets allows to reveal fractal structures, singularities etc. Wavelet transform of operator expressions helps solve some equations. In practical applications one deals often with the discretized functions, and the problem of stability of wavelet transform and corresponding numerical algorithms becomes important. After discussing all these topics we turn to practical applications of the wavelet machinery. They are so numerous that we have to limit ourselves by some examples only. The authors would be grateful for any comments which improve this review paper and move us closer to the goal proclaimed in the first phrase of the abstract.

73 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202320
202252
202159
202070
201969
201879