Related papers: Wavelets centered on a knot sequence: theory, cons…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
Capturing solution near the singular point of any nonlinear SBVPs is challenging because coefficients involved in the differential equation blow up near singularities. In this article, we aim to construct a general method based on…
The theory of orthonormal wavelet bases is a useful tool in multifractal analysis, as it provides a characterization of the different exponents of pointwise regularities (H{\"o}lder, p-exponent, lacunarity, oscillation, etc.). However, for…
Adapting the recently developed randomized dyadic structures, we introduce the notion of spline function in geometrically doubling quasi-metric spaces. Such functions have interpolation and reproducing properties as the linear splines in…
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…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, according to variational approach we obtain a…
We present a construction of a wavelet-type orthonormal basis for the space of radial $L^2$-functions in $\R^3$ via the concept of a radial multiresolution analysis. The elements of the basis are obtained from a single radial wavelet by…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
In this work, we prove that certain L^2-unbounded transformations of orthogonal wavelet bases generate vaguelets. The L^2-unbounded functions involved in the transformations are assumed to be quasi-homogeneous at high frequencies. We…
Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…
We construct spherical wavelets based on approximate identities that are directional, i.e. not rotation-invariant, and have an adaptive angular selectivity. The problem of how to find a proper representation of distinct kinds of details of…
Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets…
The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…