Related papers: Polar Wavelets in Space
Polarization observations yield otherwise unobtainable information about the geometrical structure of unresolved objects. In this talk we review the evidences for non-spherically symmetric structures around Luminous Hot Stars from…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
In this paper it is shown how one can use Bessel beams to obtain a stationary localized wavefield with high transverse localization, and whose longitudinal intensity pattern can assume any desired shape within a chosen interval 0 < z < L of…
A realistic one-dimensional system has not only longitudinal phonons, but also possible transverse modes, which derive their restoring force from longitudinal interaction. We show that transverse motion results in a quartic displacement…
Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth…
In recent times, we experimentally realized a quite efficient modeling of the shape of diffraction-resistant optical beams; thus generating for the first time the so-called Frozen Waves (FW), whose longitudinal intensity pattern can be…
Optical interferometry has made tremendous development in fundamentals and applications of light. Traditional optical interferometry using simplex plane phase light just allows one dimensional measurement, but incapable of retrieving…
Shearlet systems have been introduced as directional representation systems, which provide optimally sparse approximations of a certain model class of functions governed by anisotropic features while allowing faithful numerical realizations…
We revisit the feasibility approach to the construction of compactly supported smooth orthogonal wavelets on the line. We highlight its flexibility and illustrate how symmetry and cardinality properties are easily embedded in the design…
The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator…
In this article, we develop a general method for constructing wavelets {|det A_j|^{1/2} g(A_jx-x_{j,k}): j in J, k in K}, on irregular lattices of the form X={x_{j,k} in R^d: j in J, k in K}, and with an arbitrary countable family of…
Wavelets have been shown to be effective bases for many classes of natural signals and images. Standard wavelet bases have the entire vector space $\mathbb R^n$ as their natural domain. It is fairly straightforward to adapt these to…
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…
This work characterizes (dyadic) wavelet frames for $L^2({\mathbb R})$ by means of spectral techniques. These techniques use decomposability properties of the frame operator in spectral representations associated to the dilation operator.…
The suite of highly confined polaritons supported by two-dimensional (2D) materials constitutes a versatile platform for nano-optics, offering the means to channel light on deep-subwavelength scales. Graphene, in particular, has attracted…
We present a technique for measuring the transverse spatial properties of an optical wavefront. Intensity and phase profiles are recovered by analysis of a series of interference patterns produced by the combination of a scanning X-shaped…
A warping operator consists of an invertible axis deformation applied either in the signal domain or in the corresponding Fourier domain. Additionally, a warping transformation is usually required to preserve the signal energy, thus…
The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…
The analysis of the fully three-dimensional and time-varying polarization characteristics of a modulated trivariate, or three-component, oscillation is addressed. The use of the analytic operator enables the instantaneous three-dimensional…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…