Related papers: Polar Wavelets in Space
Wavelet and frames have become a widely used tool in mathematics, physics, and applied science during the last decade. This article gives an overview over some well known results about the continuous and discrete wavelet transforms and…
A set of orthogonal polynomials on the unit disk $B(0,1)$ known as Zernike polynomials are commonly used in the analysis and evaluation of optical systems. Here Zernike polynomials are used to construct wavelets for polynomial subspaces of…
Light transport in a highly multimode fiber exhibits complex behavior in space, time, frequency and polarization, especially in the presence of mode coupling. The newly developed techniques of spatial wavefront shaping turn out to be highly…
We introduce a novel method for directional-field design on meshes, enabling users to specify singularities at any location on a mesh. Our method uses a piecewise power-linear representation for phase and scale, offering precise control…
There are investigated amplitude-phase method of the moving object bearing when there are used orthogonal linear polarized radio signals illuminated simultaneously from two horizontally spaced points with known co-ordinates. The bearing is…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
We introduce a fast Fourier transform on regular d-dimensional lattices. We investigate properties of congruence class representants, i.e. their ordering, to classify directions and derive a Cooley-Tukey-Algorithm. Despite the fast Fourier…
The use of structured ultrashort pulses with coupled spatiotemporal properties is emerging as a key tool for ultrafast manipulation. Ultrafast vector beams are opening exciting opportunities in different fields such as microscopy,…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
A new technique based on superposition of two speckle patterns is proposed and demonstrated for controlled modulation of the spatial polarization distribution of the resultant speckle. It is demonstrated both theoretically and…
Polarforming has emerged as a promising technique to enable the antenna to shape its polarization into a desired state for aligning with that of the received electromagnetic (EM) wave or reconfiguring that of the transmitted EM wave. In…
We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional…
Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…
We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in…
We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal…
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…
We present an analytical framework capable of describing spin-waves dynamic in magnetic hetero-structures composed of a pair of exchange-decoupled magnetic layers separated by a nonmagnetic spacer, focusing in particular on garnet-based…
Dimensionality reduction of ECG signals is considered within the framework of sparse representation. The approach constructs the signal model by selecting elementary components from a redundant dictionary via a greedy strategy. The proposed…
We proved that for any matrix dilation and for any positive integer $n$, there exists a compactly supported tight wavelet frame with approximation order $n$. Explicit methods for construction of dual and tight wavelet frames with a given…