Related papers: Angular multiselectivity with spherical wavelets
The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multi-scale representation of quantum many-body wavefunctions using unitary…
We present the first wavelet-based all-electron density-functional calculations to include gradient corrections and the first in a solid. Direct comparison shows this approach to be unique in providing systematic ``transparent''…
Consider a singularly perturbed system $$\epsilon u_t=\epsilon^2 u_{xx} + f(u,x,\epsilon),\quad u\in {\Bbb R}^n,x\in{\Bbb R},t\geq 0. $$ Assume that the system has a sequence of regular and internal layers occurring alternatively along the…
Due to the current lack of large-scale datasets at the million-scale level, tasks involving panoramic images predominantly rely on existing two-dimensional pre-trained image benchmark models as backbone networks. However, these networks are…
In this article, we introduce and study the concept of $\textit{spherical-vectors}$, which can be perceived as a natural extension of the arguments of complex numbers in the context of quaternions. We initially establish foundational…
We introduce and study the property of orthogonal independence, a restricted additivity axiom applying when alternatives are orthogonal. The axiom requires that the preference for one marginal change over another should be maintained after…
Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case,…
We derive optimal filters on the sphere in the context of detecting compact objects embedded in a stochastic background process. The matched filter and the scale adaptive filter are derived on the sphere in the most general setting,…
We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. Special attention is given to the cases where the s-orbits are symmetric.
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…
We present the application of the variational-wavelet analysis to the analysis of quantum ensembles in Wigner framework. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points.…
A fast algorithm for Antoine and Vandergheynst's (1998) directional continuous spherical wavelet transform (CSWT) is presented. Computational requirements are reduced by a factor of O(\sqrt{N}), when N is the number of pixels on the sphere.…
Imaging an object embedded within a scattering medium requires the correction of complex sample-induced wave distortions. Existing approaches have been designed to resolve them by optimizing signal waves recorded in each 2D image. Here, we…
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…
Starting from a variational formulation, we present a model for image segmentation that employs both region statistics and edge information. This combination allows for improved flexibility, making the proposed model suitable to process a…
Small form-factor, narrowband, and highly directive antennas are of critical importance in a variety of applications spanning wireless communications, remote sensing, Raman spectroscopy, and single photon emission enhancement. Surprisingly,…
An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…
A new resolution enhancement method is presented for multispectral and multi-resolution images, such as these provided by the Sentinel-2 satellites. Starting from the highest resolution bands, band-dependent information (reflectance) is…
Texture characterization is a central element in many image processing applications. Multifractal analysis is a useful signal and image processing tool, yet, the accurate estimation of multifractal parameters for image texture remains a…
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…