Topic
Harmonic wavelet transform
About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.
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01 Jan 2007
TL;DR: In this article, a special member of the emerging family of multiscale geometric transforms is the curvelet transform which was developed in the last few years in an attempt to overcome inherent limitations of traditional multistage representations such as wavelets.
Abstract: A special member of the emerging family of multiscale geometric transforms is the curvelet transform which was developed in the last few years in an attempt to overcome inherent limitations of traditional multistage representations such as wavelets The Computer Tomography images were denoised using both wavelet and curvelet transform and results are presented in this paper It has been found that the cuvelet transform outperforms the wavelet transform in terms of signal noise ratio
55 citations
15 Mar 1994
TL;DR: In this paper, the authors developed outlier resistant wavelet transforms, in which outliers and outlier patches are localized to just a few scales, and improved upon the Donoho and Johnstone nonlinear signal extraction methods.
Abstract: In a series of papers, Donoho and Johnstone develop a powerful theory based on wavelets for extracting non-smooth signals from noisy data. Several nonlinear smoothing algorithms are presented which provide high performance for removing Gaussian noise from a wide range of spatially inhomogeneous signals. However, like other methods based on the linear wavelet transform, these algorithms are very sensitive to certain types of non-Gaussian noise, such as outliers. In this paper, we develop outlier resistant wavelet transforms. In these transforms, outliers and outlier patches are localized to just a few scales. By using the outlier resistant wavelet transform, we improve upon the Donoho and Johnstone nonlinear signal extraction methods. The outlier resistant wavelet algorithms are included with the 'S+WAVELETS' object-oriented toolkit for wavelet analysis.
55 citations
TL;DR: Comparison against the more widely-used multitaper Fourier transform approach shows that the enhanced wavelet method not only improves upon the multitaper method's spatial resolution, but also is computationally much faster and requires the arbitrary variation of only one parameter compared to three for the multitapers.
55 citations
01 Jan 2008
TL;DR: In this article, the authors proposed a multiresolution analysis that reexpresses a time series as the sum of several new series, each of which is associated with a particular scale.
Abstract: Discrete wavelet transforms (DWTs) are mathematical tools that are useful for analyzing geophysical time series The basic idea is to transform a time series into coefficients describing how the series varies over particular scales One version of the DWT is the maximal overlap DWT (MODWT) The MODWT leads to two basic decompositions The first is a scale-based analysis of variance known as the wavelet variance, and the second is a multiresolution analysis that reexpresses a time series as the sum of several new series, each of which is associated with a particular scale Both decompositions are illustrated through examples involving Arctic sea ice and an Antarctic ice core A second version of the DWT is the orthonormal DWT (ODWT), which can be extracted from the MODWT by subsampling The relative strengths and weaknesses of the MODWT, the ODWT and the continuous wavelet transform are discussed
55 citations
13 Nov 1994
TL;DR: Experimental results demonstrate the flexibility to selectively enhance features of different sizes and ability to control noise magnification of the new multiscale gradient transformation method.
Abstract: We present a new technique for image contrast enhancement via multiscale gradient transformation In contrast to histogram-based techniques which aim to change the global statistical distribution of pixel intensities, we improve image contrast by modifying the modulus of the gradient image at multiple scales In computation, a multiscale gradient representation of the image is generated by a wavelet transform (WT) Linear or nonlinear transformation is applied to multiscale gradients A contrast-enhanced image is obtained from the transformed multiscale gradients by the inverse wavelet transform Experimental results demonstrate two advantages of the new method: its flexibility to selectively enhance features of different sizes and ability to control noise magnification >
54 citations