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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kahler geometry methods in Gaussian Gabor frame theory
高斯 Gabor框架理论 Kahler几何
2023/11/6
We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kahler geometry such as Hormander's $\dbar$-L2 estimate with singular weight, Demailly's Calabi--Yau metho...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Exponential mixing of frame flows for geometrically finite hyperbolic manifolds with cusps
几何有限 双曲流形带尖 框架流 指数混合
2023/4/28
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Exponential mixing of frame flows for geometrically finite hyperbolic manifolds with cusps
几何有限 双曲流形带尖 框架流 指数混合
2023/5/4
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
PRECONDITIONING TECHNIQUES IN FRAME THEORY AND PROBABILISTIC FRAMES
Parseval frame Scalable frame Fritz John Theorem Probabilistic frames frame potential continuous frames
2015/12/10
In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames.These are (finite) frames with the property that e...
FRAME POTENTIAL AND FINITE ABELIAN GROUPS
tight frame frame potential finite abelian group sampling
2015/12/10
This article continues a prior investigation of the authors with the goal of extending characterization results of convolutional tight frames from the context of cyclic groups to general finite abelia...
Minimization of the Probabilistic p-frame Potential
Frame potential equiangular tight frames probabilistic frames
2015/12/10
We investigate the optimal configurations of n points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of theirapproximation ...
INVERTIBILITY OF THE GABOR FRAME OPERATOR ON THE WIENER AMALGAM SPACE
Wiener amalgam space Gabor frame Walnut representation Wiener’s Lemma
2015/12/10
We use a generalization of Wiener’s 1/f theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space W (L∞, `1 )(Rd), the corresponding frame operator is invertible on this s...
A Nonlinear Reconstruction Algorithm from Absolute Value of Frame Coefficients for Low Redundancy Frames
Nonlinear Reconstruction Algorithm Absolute Value of Frame Coefficients Low Redundancy Frames
2015/9/29
In this paper we present a signal reconstruction algorithm from absolute value of frame coefficients that requires arelatively low redundancy. The basic idea is to use a nonlinear embedding of the inp...
PAINLESS RECONSTRUCTION FROM MAGNITUDES OF FRAME COEFFICIENTS
PAINLESS RECONSTRUCTION FRAME COEFFICIENTS
2015/9/29
The primary goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients. This problem is important to several areas of research in signal processin...
Equivalence of Reconstruction from the Absolute Value of the Frame Coefficients to a Sparse Representation Problem
frames nonlinear processing sparse representation
2015/9/29
The purpose of this note is to prove, for real frames, that signal reconstruction from the absolute value ofthe frame coefficients is equivalent to solution of a sparse signal optimization problem, na...
Painless Reconstruction from Magnitudes of Frame Coefficients
Frames Reconstruction without phase Projective 2-designs
2015/9/29
The goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients.This problem is important to several areas of research in signal processing, especi...
Abstract: In information fusion, one is often confronted with the following problem: given a preexisting set of measurements about an unknown quantity, what new measurements should one collect in orde...
Constructing pairs of dual bandlimited frame wavelets in $L^2(\mathbb{R}^n)$
real and expansive dilation matrix bandlimited wavelets dual frames
2010/12/10
Given a real, expansive dilation matrix we prove that any bandlimited function ∈ L2(Rn), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for cer...
Classification of General Sequences by Frame-Related Operators
analysis operator synthesis operator frame op-erator Gram matrix Bessel sequence
2010/12/1
This note is a survey and collection of results, as well as present-ing some original research. For Bessel sequences and frames, the analy-sis, synthesis and frame operators as well as the Gram matrix...
An asymptotic equivalence between two frame perturbation theorems
asymptotic equivalence two frame perturbation theorems
2010/12/3
In this paper, two stability results regarding exponential frames are compared.The theorems, (one proven herein, and the other in [3]), each give a constant such that if supn∈Z kenk¥ < C, and (eih...