منابع مشابه
Image processing by alternate dual Gabor frames
We present an application of the dual Gabor frames to image processing. Our algorithm is based on finding some dual Gabor frame generators which reconstructs accurately the elements of the underlying Hilbert space. The advantages of these duals constructed by a polynomial of Gabor frame generators are compared with their canonical dual.
متن کاملThe Density Theorem and the Homogeneous Approximation Property for Gabor Frames
The Density Theorem for Gabor Frames is a fundamental result in timefrequency analysis. Beginning with Baggett’s proof that a rectangular lattice Gabor system {eg(t−αk)}n,k∈Z must be incomplete in L (R) whenever αβ > 1, the necessary conditions for a Gabor system to be complete, a frame, a Riesz basis, or a Riesz sequence have been extended to arbitrary lattices and beyond. The first partial pr...
متن کاملHistory and Evolution of the Density Theorem for Gabor Frames
The Density Theorem for Gabor Frames is one of the fundamental results of time-frequency analysis. This expository survey attempts to reconstruct the long and very involved history of this theorem and to present its context and evolution, from the onedimensional rectangular lattice setting, to arbitrary lattices in higher dimensions, to irregular Gabor frames, and most recently beyond the setti...
متن کاملDensity, Overcompleteness, and Localization of Frames
This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown betwee...
متن کاملDensity, Overcompleteness, and Localization of Frames. Ii. Gabor Systems
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 = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. This article shows that those ab...
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تاریخ انتشار 1999