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.

Besov norms in terms of the continuous wavelet transform. application to structure functions

Abstract: The continuous wavelet transform is extended to Lp spaces and an inversion formula is demonstrated. From this the Besov spaces can be characterized by the behavior at small scales of the wavelet coefficients. These results apply to the measurement of structure functions.

Instantaneous polarization attributes in the time-frequency domain and wavefield separation

Abstract: We introduce a method of wavefield separation from multicomponent data sets based on the use of the continuous wavelet transform. Our method is a further generalization of the approach proposed by Morozov and Smithson, in that by using the continuous wavelet transform, we can achieve a better separation of wave types by designing the filter in the time–frequency domain. Furthermore, using the instantaneous polarization attributes defined in the wavelet domain, we show how to construct filters tailored to separate different wave types (elliptically or linearly polarized), followed by an inverse wavelet transform to obtain the desired wave type in the time domain. Using synthetic and experimental data, we show how the present method can be used for wavefield separation.

Multivariate spectral analysis using hilbert wavelet pairs

Abstract: We investigate the use of Hilbert wavelet pairs (HWPs) in the non-decimated discrete wavelet transform for the time-varying spectral analysis of multivariate time series. HWPs consist of two high-pass and two low-pass compactly supported filters, such that one high-pass filter is the Hilbert transform (approximately) of the other. Thus, common quantities in the spectral analysis of time series (e.g., power spectrum, coherence, phase) may be estimated in both time and frequency. Compact support of the wavelet filters ensures that the frequency axis will be partitioned dyadically as with the usual discrete wavelet transform. The proposed methodology is used to analyze a bivariate time series of zonal (u) and meridional (v) winds over Truk Island.

Applications of Gabor and wavelet expansions to the Radon transform

Abstract: We investigate the relationship between the Radon transform and certain phase space localization functions, namely the continuous Gabor and wavelet transforms. We derive inversion formulas for the Radon transform based on the Gabor and wavelet transform. Some of these formulas give a direct reconstruction of f or of Δ1/2f from the Radon transform data. Others show how the Gabor and wavelet transforms of f or Δ1/2f can be recovered directly from the Radon transform data. We suggest ways in which these formulas can lead to efficient reconstruction algorithms and can be applied to noise reduction in reconstructed images.

Image reconstruction by the wavelet transform applied to aperture synthesis

Abstract: The Wavelet Transform is a tool which allows us to get information both in the direct space and in the frequency space. We have developed an algorithm based on the FFT with an isotropic wavelet. A multiresolution deconvolution is performed for the interferometric images by using the CLEAN method on the wavelet coefficients. An iterative reconstruction assumes the existence of a solution which satisfies the positivity and the limited support constraints, and which is compatible with the measured visibilities. By this method, the images of two evolved stars have been reconstructed from infrared speckle interferometry observations