Approximation of the Inverse Frame Operator and Applications to Gabor Frames

By Peter G. Casazza, Ole W. Christensen. 2000

62 citations recorded by the source corpus.

A frame allows every element in a Hilbert space H to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculation of the frame coefficients requires inversion of an operator S on H. We show how the inverse of S can be approximated as close as we like using finite-dimensional linear algebra. In contrast with previous methods, our approximation can be used for any frame. Various consequences for approximation of the frame coefficients or approximation of the solution to a moment problem are discussed. We also apply the results to Gabor frames and frames consisting of translates of a single function.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Geophysics

View Paper: https://www.semanticscholar.org/paper/6f805671f937338050da339d7146c9c8ba6532e0

Citations in the corpus

• Approximation of the Fourier Transform and the Dual Gabor Window (2005, unknown): “projection method [6, 7], see [9, Section 16.”