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Continuous wavelet transform

About: Continuous wavelet transform is a research topic. Over the lifetime, 6064 publications have been published within this topic receiving 109622 citations. The topic is also known as: CWT.


Papers
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Journal ArticleDOI
TL;DR: The author describes the mathematical properties of such decompositions and introduces the wavelet transform, which relates to the decomposition of an image into a wavelet orthonormal basis.
Abstract: The author reviews recent multichannel models developed in psychophysiology, computer vision, and image processing. In psychophysiology, multichannel models have been particularly successful in explaining some low-level processing in the visual cortex. The expansion of a function into several frequency channels provides a representation which is intermediate between a spatial and a Fourier representation. The author describes the mathematical properties of such decompositions and introduces the wavelet transform. He reviews the classical multiresolution pyramidal transforms developed in computer vision and shows how they relate to the decomposition of an image into a wavelet orthonormal basis. He discusses the properties of the zero crossings of multifrequency channels. Zero-crossing representations are particularly well adapted for pattern recognition in computer vision. >

2,109 citations

Journal ArticleDOI
TL;DR: The conditions under which a set of continuous 2D Gabor wavelets will provide a complete representation of any image are derived, and self-similar wavelet parametrization is found which allow stable reconstruction by summation as though the wavelets formed an orthonormal basis.
Abstract: This paper extends to two dimensions the frame criterion developed by Daubechies for one-dimensional wavelets, and it computes the frame bounds for the particular case of 2D Gabor wavelets. Completeness criteria for 2D Gabor image representations are important because of their increasing role in many computer vision applications and also in modeling biological vision, since recent neurophysiological evidence from the visual cortex of mammalian brains suggests that the filter response profiles of the main class of linearly-responding cortical neurons (called simple cells) are best modeled as a family of self-similar 2D Gabor wavelets. We therefore derive the conditions under which a set of continuous 2D Gabor wavelets will provide a complete representation of any image, and we also find self-similar wavelet parametrization which allow stable reconstruction by summation as though the wavelets formed an orthonormal basis. Approximating a "tight frame" generates redundancy which allows low-resolution neural responses to represent high-resolution images.

1,727 citations

Book
01 Jul 1988
TL;DR: This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.
Abstract: The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.

1,432 citations

Journal ArticleDOI
TL;DR: This paper presents a new approach to build adaptive wavelets, the main idea is to extract the different modes of a signal by designing an appropriate wavelet filter bank, which leads to a new wavelet transform, called the empirical wavelets transform.
Abstract: Some recent methods, like the empirical mode decomposition (EMD), propose to decompose a signal accordingly to its contained information. Even though its adaptability seems useful for many applications, the main issue with this approach is its lack of theory. This paper presents a new approach to build adaptive wavelets. The main idea is to extract the different modes of a signal by designing an appropriate wavelet filter bank. This construction leads us to a new wavelet transform, called the empirical wavelet transform. Many experiments are presented showing the usefulness of this method compared to the classic EMD.

1,398 citations

Book
01 Jan 1994
TL;DR: This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data.
Abstract: This detail-oriented text is intended for engineers and applied mathematicians who must write computer programs to perform wavelet and related analysis on real data. It contains an overview of mathematical prerequisites and proceeds to describe hands-on programming techniques to implement special programs for signal analysis and other applications. From the table of contents: - Mathematical Preliminaries - Programming Techniques - The Discrete Fourier Transform - Local Trigonometric Transforms - Quadrature Filters - The Discrete Wavelet Transform - Wavelet Packets - The Best Basis Algorithm - Multidimensional Library Trees - Time-Frequency Analysis - Some Applications - Solutions to Some of the Exercises - List of Symbols - Quadrature Filter Coefficients

1,292 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202335
202280
2021145
2020151
2019176
2018183