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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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Journal Article
TL;DR: Drawing a conclusion that application of wavelet analysis is effective on the aspect of singularity measurement, the Mallat algorithm has been introduced and applied on signal analysis and disposal.
Abstract: With the development of Fourier analysis,wavelet analysis become the concerned question of many subjects.On the basis of conception of wavelet transform,the Mallat algorithm has been introduced and applied on signal analysis and disposal,so a failure signal can been decomposed and restructured.Through analysis of experiment,the high frequency part can reflect the turning point,and the position of fault-point can be gained by the important information,so drew a conclusion that application of wavelet analysis is effective on the aspect of singularity measurement.

90 citations

Journal ArticleDOI
TL;DR: The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform, providing new insight into wave propagation and spherical mirror resonators.
Abstract: The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to the Gouy phase shift between the two surfaces. This result provides new insight into wave propagation and spherical mirror resonators as well as the possibility of exploiting the fractional Fourier transform as a mathematical tool in analyzing such systems.

90 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduced a wavelet transform technique based on the detection of the multi-scale view of the components of a signal, which can be used for space-frequency localization and analysis of roughness and waviness motifs.
Abstract: This work introduces a wavelet transform technique based on the detection of the multi-scale view of the components of a signal . The main advantages of wavelet transform over the existing signal processing techniques are its space-frequency localization and multi-scale analysis of roughness and waviness motifs. After an extensive review of the mathematical and signal processing fundamentals of the wavelet technique, numerical implementations are carried out to explore the potential applications of wavelet transform and its inverse transform multi-scale analysis of roughness and local morphological characterization by the detection of the roughness singularities and 21) motif size of an engineered surface.

90 citations

Journal ArticleDOI
TL;DR: An unconstrained, TV-regularized, $\ell_2$-data-fitting model to recover the image, solved by the alternating direction method (ADM), and extensions of this ADM scheme to solving two closely related constrained models.
Abstract: Image inpainting in wavelet domains refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature, and they produce high-quality reconstructed images. In this paper, we consider an unconstrained, TV-regularized, $\ell_2$-data-fitting model to recover the image. The model is solved by the alternating direction method (ADM). At each iteration, the ADM needs to solve three subproblems, all of which have closed-form solutions. The per-iteration computational cost of the ADM is dominated by two Fourier transforms and two wavelet transforms, all of which admit fast computation. Convergence of the ADM iterative scheme is readily obtained. We also discuss extensions of this ADM scheme to solving two closely related constrained models. We present numerical results to show the efficiency and stability of the ADM for solving wavelet domain image inpainting problems. Numerical results comparing the ADM with some recent algorithms are also reported.

89 citations

BookDOI
01 Jan 1995

89 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202323
202274
20213
20207
20196
201831