Related papers: Multidimensional Wavelets for Scalable Image Decom…
This paper investigates the potential applications of a parametric family of polynomial wavelets that has been recently introduced starting from de la Vall\'ee Poussin (VP) interpolation at Chebyshev nodes. Unlike classical wavelets, which…
Multidimensional imaging, capturing image data in more than two dimensions, has been an emerging field with diverse applications. Due to the limitation of two-dimensional detectors in obtaining the high-dimensional image data, computational…
Aims: We discuss the applicability and reliability of the shapelet technique for scientific image analysis. Methods: We quantify the effects of non-orthogonality of sampled shapelet basis functions and misestimation of shapelet parameters.…
We present a wavelet-based dual-stream network that addresses color cast and blurry details in underwater images. We handle these artifacts separately by decomposing an input image into multiple frequency bands using discrete wavelet…
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
This paper offers a new regard on compactly supported wavelets derived from FIR filters. Although being continuous wavelets, analytical formulation are lacking for such wavelets. Close approximations for daublets (Daubechies wavelets) and…
We construct a multiresolution theory for spaces bigger then L^2(R). For a good choice of the dilation and translation operators on these larger spaces, it is possible to build singly generated wavelet bases, thus obtaining examples of…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
We propose a method for obtaining the Schmidt decomposition of bipartite systems with continuous variables. It approximates the modes to the prescribed accuracy by well known orthogonal functions. We give some criteria for the control of…
In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by…
We have found a new class of time dependent partial waves which are solutions of time dependent Schr\"odinger equation for three dimensional harmonic oscillator. We also showed the decomposition of coherent states of harmonic oscillator…
Three-dimensional elements, with refractive index distribution structured at sub-wavelength scale, provide an expansive optical design space that can be harnessed for demonstrating multi-functional free-space optical devices. Here we…
We consider the problem of atmospheric tomography, as it appears for example in adaptive optics systems for extremely large telescopes. We derive a frame decomposition, i.e., a decomposition in terms of a frame, of the underlying…
The concept of correlated two-photon spiral imaging is introduced. We begin by analyzing the joint orbital angular momentum (OAM) spectrum of correlated photon pairs. The mutual information carried by the photon pairs is evaluated, and it…
Orbital magnetic susceptibility involves rich physics such as interband effects despite of its conceptual simplicity. In order to appreciate the rich physics related to the orbital magnetic susceptibility, it is essential to derive a…
We demonstrate how the image analysis technique of wavelet decomposition can be applied to the gamma-ray sky to separate emission on different angular scales. New structures on scales that differ from the scales of the conventional…
The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from…
Fusion frames are a convenient tool in applications where we deal with a large amount of data or when a combination of local data is needed. Oblique dual fusion frames are suitable in situations where the analysis for the data and its…
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…
We first extend our recent experiments of correlation imaging through scattering media to the case of a thick medium, composed of two phase scatterers placed respectively in the image and the Fourier planes of the crystal. The spatial…