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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...
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight...
MULTI-WINDOW GABOR FRAMES IN AMALGAM SPACES
Wiener amalgam space Gabor frame Wiener’s Lemma
2015/12/10
We show that multi-window Gabor frames with windows in the Wiener algebra W(L∞, `1) are Banach frames for all Wiener amalgam spaces. As a by-product of our results we prove thecanonical dual of a Gabo...
The objective of this paper is the linear reconstruction of a vector, up to a unimodular constant, when all phase information is lost, meaning only the magnitudes of frame coefficients are known. Reco...
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...
Stability Theorems for Fourier Frames and Wavelet Riesz Bases
Frames Riesz basis nonharmonic series wavelets
2015/9/29
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type co...
A NEW IDENTITY FOR PARSEVAL FRAMES
Bessel sequence Frame Hilbert space Parseval frame Parseval Frame Identity
2015/9/29
In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss ...
In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set F of m vectors in the complex Hilber...
Stability of Phase Retrievable Frames
Frames phase retrieval problem perturbations critical redundancy
2015/9/29
In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set F of m vectors in the complex Hilber...
Preconditioners based on Windowed Fourier Frames Applied to Elliptic Partial Differential Equations
Windowed Fourier frame symbol elliptic PDE preconditioner
2010/12/3
We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial di erential equations, focussing on elliptic equations. The action of a partial di erential operat...
This paper addresses the construction of wavelet frame from a {\it frame multiresolution analysis} ({\bf FMRA}) associated with a dilation matrix of determinant $\pm 2$. The dilation matrices of deter...