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Frames which are tight might be considered optimally conditioned in the sense of their numerical stability.This leads to the question of perfect preconditioning of frames,i.e., modification of a given...
Prime tight frames
divisible frames equiangular tight frames frames harmonic tight frames prime frames spectral tetris frames tight frames
2015/12/10
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of pri...
FINITE TWO-DISTANCE TIGHT FRAMES
Spherical two-distance sets finite tight frames strongly regular graphs spherical 2-designs spherical designs of harmonic index 2
2015/12/10
A finite collection of unit vectors S ⊂ Rn is called a spherical two-distance set if there are two numbers a and b such that the inner products of distinct vectors from S are either a or b. We p...
Deficits and Excesses of Frames
Bessel sequences deficit excess frames Gabor systems Riesz bases wavelets Weyl–Heisenberg systems
2015/9/29
The excess of a sequence in a Hilbert space is the greatest number of elements that can be removed yet leave a set with the same closed span. We study the excess and the dual concept of the deficit of...
Density,Overcompleteness,and Localization of Frames.I.Theory
Density excess frames Gabor systems modulation spaces overcompleteness Riesz bases wavelets Weyl–Heisenberg systems
2015/9/29
Frames have applications in numerous fields of mathematics and engineering.The fundamental property of frames which makes them so useful is their overcompleteness.In most applications, it is this over...
Density, Overcompleteness,and Localization of Frames.II.Gabor Systems
Density excess frames Gabor systems modulation spaces overcompleteness Riesz bases wavelets Weyl–Heisenberg systems
2015/9/29
This work develops a quantitative framework for describing the overcompleteness of a large class of frames. A previous article introduced notions of localization and approximation between two frames F...
FRAMES AND PHASELESS RECONSTRUCTION AMS SHORT COURSE:JOINT MATHEMATICS MEETINGS SAN ANTONIO,2015
FRAMES AND PHASELESS RECONSTRUCTION AMS SHORT COURSE JOINT MATHEMATICS MEETINGS SAN ANTONIO
2015/9/29
Frame design for phaseless reconstruction is now part of the broader problem of nonlinear recon- struction and is an emerging topic in harmonic analysis. The problem of phaseless reconstruction can be...
New Tight Frames of Curvelets and Optimal Representations of Objects with C2 Singularities
Curvelets wavelets second dyadic decomposition edges nonlinear approximation singularities thresholding Radon transform
2015/6/17
This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges.Conceptually, the curvelet transfo...
Continuous Curvelet Transform:II. Discretization and Frames
Curvelets Parabolic Scaling Fourier Integral Operator Tight Frame
2015/6/17
We develop a unifying perspective on several decompositions exhibiting directional parabolic scaling. In each decomposition, the individual atoms are highly anisotropic at fine scales, with effective ...
Non-orthogonal fusion frames and the sparsity of fusion frame operators
Frames Fusion Frames Sparsity Fusion Frame Operator
2011/1/19
Fusion frames have become a major tool in the implemen-tation of distributed systems. The effectiveness of fusion frame appli-cations in distributed systems is reflected in the efficiency of the end f...
Frames and finite dimensionality: Frame transformation, classification and algorithms
frame inequality discrete expansion matrices
2010/9/14
In this paper we will look at the connection of frames and finite dimensionality. The focus is to present simple algorithms, which are available online. We will give basic algorithms to use with frame...