Related papers: The continuous wavelet derived by smoothing functi…
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
Recently, it has been proven [R. Soc. Open Sci. 1 (2014) 140124] that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows for an existence of the exact inverse transform. Here we consider the…
A fast algorithm for Antoine and Vandergheynst's (1998) directional continuous spherical wavelet transform (CSWT) is presented. Computational requirements are reduced by a factor of O(\sqrt{N}), when N is the number of pixels on the sphere.…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
A novel wavelet-like function is presented that makes it convenient to create filter banks given mainly two parameters that influence the focus area and the filter count. This is accomplished by computing the inverse Fourier transform of…
This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…
This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…
In this paper we propose a new adaptive wavelet denoising methodology using complex wavelets. The method is based on a fully Bayesian hierarchical model in the complex wavelet domain that uses a bivariate mixture prior on the wavelet…
An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate…
Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…
This note is devoted to an analysis of the so-called peeling algorithm in wavelet denoising. Assuming that the wavelet coefficients of the signal can be modeled by generalized Gaussian random variables, we compute a critical thresholding…
We propose the multiview wavelets based on voxel patterns of autostereoscopic multiview displays. Direct and inverse continuous wavelet transforms of binary and gray-scale images were performed. The input to the inverse wavelet transform…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
Mesoscale structures can often be described as fractional dimensional across a wide range of scales. We consider a $\gamma$ dimensional measure embedded in an $N$ dimensional space and discuss how to determine its dimension, both in $N$…
Morlet or Gabor wavelet transforms as well as Gaussian smoothing, are widely used in signal processing and image processing. However, the computational complexity of their direct calculations is proportional not only to the number of data…
Continuing our recent work we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the…
In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical…
The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the admissibility condition. We propose an alternative…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…