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Wavelet packet decomposition

About: Wavelet packet decomposition is a research topic. Over the lifetime, 21977 publications have been published within this topic receiving 395949 citations.


Papers
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Book ChapterDOI
01 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.

1,888 citations

Journal ArticleDOI
TL;DR: It is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support.
Abstract: Two separately motivated implementations of the wavelet transform are brought together. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by the choice of filters. In fact, the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, it is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the discrete wavelet transform is provided, and conditions are derived under which it computes the continuous wavelet transform exactly. Suitable filter constraints for finite energy and boundedness of the discrete transform are also derived. Relevant signal processing parameters are examined, and it is observed that orthonormality is balanced by restrictions on resolution. >

1,856 citations

Journal ArticleDOI
TL;DR: In this article, a dual tree of wavelet filters is proposed to obtain real and imaginary parts of the wavelet transform. And the dual tree can be extended for image and other multi-dimensional signals.

1,767 citations

Journal ArticleDOI
TL;DR: This paper introduces a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and proves that the method does indeed succeed in decomposing arbitrary functions in this class.

1,704 citations

Journal ArticleDOI
TL;DR: Most major filtering approaches to texture feature extraction are reviewed and a ranking of the tested approaches based on extensive experiments is presented, showing the effect of the filtering is highlighted, keeping the local energy function and the classification algorithm identical for most approaches.
Abstract: In this paper, we review most major filtering approaches to texture feature extraction and perform a comparative study. Filtering approaches included are Laws masks (1980), ring/wedge filters, dyadic Gabor filter banks, wavelet transforms, wavelet packets and wavelet frames, quadrature mirror filters, discrete cosine transform, eigenfilters, optimized Gabor filters, linear predictors, and optimized finite impulse response filters. The features are computed as the local energy of the filter responses. The effect of the filtering is highlighted, keeping the local energy function and the classification algorithm identical for most approaches. For reference, comparisons with two classical nonfiltering approaches, co-occurrence (statistical) and autoregressive (model based) features, are given. We present a ranking of the tested approaches based on extensive experiments.

1,567 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202379
2022207
2021192
2020211
2019288
2018339