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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.


Papers
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Journal ArticleDOI
TL;DR: The wavelet transform is a recent method of signal analysis and synthesis that analyzes signals in terms of wavelets-functions limited both in the time and the frequency domain in comparison to the classical Fourier analysis method.
Abstract: The wavelet transform is a recent method of signal analysis and synthesis (Grossmann and Morlet 1984; Grossmann et al. 1987). It analyzes signals in terms of wavelets-functions limited both in the time and the frequency domain. In comparison, the classical Fourier analysis method analyzes signals in terms of sine and cosine wave components that are not limited in time. The wavelet transform is related to granular analysis/synthesis, first suggested by Gabor (1946). Granular synthesis has been implemented by Roads (1978) and Truax (1988). Rodet (1985) and Li6nard (1984) use adapted grains for speech signals; however, these implementations do not attempt to reconstruct an arbitrary given signal. The Gabor method uses an expansion of a function into a two-parameter family of elementary wavelets that are obtained from one basic wavelet

108 citations

Journal ArticleDOI
TL;DR: A particularly simple way to control fast Fourier transform (FFT) hardware that allows parallel organization of the memory such that at any stage the two inputs and outputs of each butterfly belong to different memory units, hence can always be accessed in parallel.
Abstract: A particularly simple way to control fast Fourier transform (FFT) hardware is described. The method produces the indices both for inputs of each butterfly operation and for the appropriate W. In addition, this method allows parallel organization of the memory such that at any stage the two inputs and outputs of each butterfly belong to different memory units, hence can always be accessed in parallel.

108 citations

Book ChapterDOI
30 Oct 2004
TL;DR: This scheme takes advantage of the Laplacian-like distribution of integer wavelet coefficients in high frequency subbands, which facilitates the selection of compression and expansion functions and keeps the distortion small between the marked image and the original one.
Abstract: This paper presents a novel reversible data-embedding method for digital images using integer wavelet transform and companding technique. This scheme takes advantage of the Laplacian-like distribution of integer wavelet coefficients in high frequency subbands, which facilitates the selection of compression and expansion functions and keeps the distortion small between the marked image and the original one. Experimental results show that this scheme outperforms the state-of-the-art reversible data hiding schemes.

107 citations

Journal ArticleDOI
TL;DR: The circular harmonic transform (CHT) solution of the exponential Randon transform (ERT) is applied to single-photon emission computed tomography (SPECT) for uniform attenuation within a convex boundary to demonstrate that the boundary conditions are a more general property of the Radon transform and a not a property unique to rectangular coordinates.
Abstract: The circular harmonic transform (CHT) solution of the exponential Randon transform (ERT) is applied to single-photon emission computed tomography (SPECT) for uniform attenuation within a convex boundary. An important special case also considered is the linear (unattenuated) Radon transform (LRT). The solution is on the form of an orthogonal function expansion matched to projections that are in parallel-ray geometry. This property allows for efficient and accurate processing of the projections with fast Fourier transform (FFT) without interpolation or beam matching. The algorithm is optimized by the use of boundary conditions on the 2-D Fourier transform of the sinogram. These boundary conditions imply that the signal energy of the sinogram is concentrated in well-defined sectors in transform space. The angle defining the sectors depends in a direct way on the radius of the field view. These results are also obtained for fan-beam geometry and the linear Radon transform (the Fourier-Chebyshev transform of the sinogram) to demonstrate that the boundary conditions are a more general property of the Radon transform and a not a property unique to rectangular coordinates. >

107 citations


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