Related papers: Discrete Directional Gabor Frames
We present a discrete theory for modeling developable surfaces as quadrilateral meshes satisfying simple angle constraints. The basis of our model is a lesser known characterization of developable surfaces as manifolds that can be…
We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to…
In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a…
We present a novel way of constructing the Gaussian Free Field on a weighted graph via a dynamical expansion of the Green function along an expanding family of subgraphs. Along the way we obtain the discrete analogue of the classical…
A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…
We analyze the interplay between contact geometry and Gabor filters signal analysis in geometric models of the primary visual cortex. We show in particular that a specific framed lattice and an associated Gabor system is determined by the…
It is known that, in general, an affine or Gabor AP-frame is an $L^2(\mathbb{R})$-frame and conversely. In part as a consequence of the Ergodic Theorem, we prove a necessary and sufficient condition for an affine (wavelet) system…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
In this paper we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g,a,b). The iterations start with the window g while the…
We develop a rigidity theory for bar-joint frameworks in Euclidean $d$-space in which specified classes of edges are allowed to change length in a coordinated fashion that requires differences of lengths to be preserved within each class.…
Presented is description of kinematics and dynamics of material points with internal degrees of freedom moving in a Riemannian manifold. The models of internal degrees of freedom we concentrate on are based on the orthogonal and affine…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
A semi-analytical computational algorithm to model the wavefield generated by paraxial diffraction of a class of Laguerre-Gauss beams by sharp-edge elliptic apertures is here developed. Thanks to such a powerful computational tool, some…
In this paper we apply the anholonomic frames method developed in refs. [1-4] to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off--diagonal 5D metric, parameterized in terms of several ansatz…
In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…
We study Gabor orthonormal windows in $L^2({\Bbb Z}_p^d)$ for translation and modulation sets $A$ and $B$, respectively, where $p$ is prime and $d\geq 2$. We prove that for a set $E\subset \Bbb Z_p^d$, the indicator function $1_E$ is a…
Isotropic positive definite functions on spheres play important roles in spatial statistics, where they occur as the correlation functions of homogeneous random fields and star-shaped random particles. In approximation theory, strictly…
We report on miniature GaAs disk optomechanical resonators vibrating in air in the radiofrequency range. The flexural modes of the disks are studied by scanning electron microscopy and optical interferometry, and correctly modeled with the…
We study symplectic deformations of Gabor frames using the covariance properties of the Heisenberg operators. This allows us to recover in a very simple way known results. We thereafter propose a general deformation scheme by Hamiltonian…