Excesses of Gabor frames

Deficits and Excesses of Frames

Radu Balan a, Peter G. Casazza b,∗, Christopher Heil c,∗∗, and Zeph Landau d a Siemens Corporate Research, Princeton, New Jersey 08540 E-mail: [email protected] b Department of Mathematics, University of Missouri, Columbia, Missouri 65211 E-mail: [email protected] c School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 E-mail: [email protected] d Mathemati...

Density of Gabor Frames

Deformations of Gabor Frames

The quantum mechanical harmonic oscillator Hamiltonian H = (t − ∂ t )/2 generates a one–parameter unitary group W (θ) = e in L(R) which rotates the time–frequency plane. In particular, W (π/2) is the Fourier transform. When W (θ) is applied to any frame of Gabor wavelets, the result is another such frame with identical frame bounds. Thus each Gabor frame gives rise to a one–parameter family of ...

Nonstationary Gabor Frames

To overcome the limitation induced by the fixed timefrequency resolution over the whole time-frequency plane of Gabor frames, we propose a simple extension of the Gabor theory leading to the construction of frames with timefrequency resolution evolving over time or frequency. We describe the construction of such frames and give the explicit formulation of the canonical dual frame for some condi...

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.