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Construction of Symmetric Complex Tight wavelet Frames from Pseudo Splines via Matrix Extension with Symmetry.
Fractional spline wavelet systems are considered in the work. Molecular structure of elements of such systems admits estimates connecting norms of fractional integrals' images and pre--images in Besov spaces.
Light scattering by two-dimensional (2D) van der Waals heterostructures (vdWHs) is immense, especially given their infinitesimal volume, thus enabling strong light-matter interactions. Surface 2D polariton waves manifest through large…
In this paper we study some problems related with the theory of multidimensional $p$-adic wavelets in connection with the theory of multidimensional $p$-adic pseudo-differential operators (in the $p$-adic Lizorkin space). We introduce a new…
In this paper, we introduce several new schemes for calculation of discrete wavelet transforms of images. These schemes reduce the number of steps and, as a consequence, allow to reduce the number of synchronizations on parallel…
We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering…
A quasislit is the image of a vertical line segment [0, iy], y > 0, under a quasiconformal homeomorphism of the upper half-plane fixing infinity. Quasislits correspond precisely to curves generated by the Loewner equation with a driving…
Polymers that extend covalently in two dimensions have attracted recent attention as a means of combining the mechanical strength and in-plane energy conduction of conventional two-dimensional (2D) materials with the low densities,…
Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two…
Upcoming LCLS-II/II-HE operation at repetition rates approaching 1MHz demands on-detector data reduction to manage the resulting data volumes. We present a 2D discrete wavelet transform (DWT) pre-processing algorithm that segments…
Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this…
Wavelet Transforms are a widely used technique for decomposing a signal into coefficient vectors that correspond to distinct frequency/scale bands while retaining time localization. This property enables an adaptive analysis of signals at…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
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…
This article presents Holistically-Attracted Wireframe Parsing (HAWP), a method for geometric analysis of 2D images containing wireframes formed by line segments and junctions. HAWP utilizes a parsimonious Holistic Attraction (HAT) field…
We represent a version of multidimensional quasilinear partial differential equation (PDE) together with large manifold of particular solutions given in an integral form. The dimensionality of constructed PDE can be arbitrary. We call it…
Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical…
Radially symmetric wavelets possessing multiresolution framework are found to be useful in different fields like Pattern recognition, Computed Tomography (CT) etc. The compactly supported wavelets are known to be useful for localized…
Wavelet set wavelets were the first examples of wavelets that may not have associated multiresolution analyses. Furthermore, they provided examples of complete orthonormal wavelet systems in $L^2(\mathbb{R}^d)$ which only require a single…
We investigate the astonishing physical aspects of Exceptional Points (EPs) in a 1D planar few-mode optical waveguide. The waveguide hosts four quasi-guided modes. Here interactions between the selected pair of modes are modulated by a…