Approximations For Gabor And Wavelet Frames
Approximation; Frames; Gabor family and Gabor frames; Hilbert spaces; Unitary systems; Wavelet frames
Let ψ be a frame vector under the action of a collection of unitary operators script U sign. Motivated by the recent work of Prank, Paulsen and Tiballi and some application aspects of Gabor and wavelet frames, we consider the existence and uniqueness of the best approximation by normalized tight frame vectors. We prove that for any frame induced by a projective unitary representation for a countable discrete group, the best normalized tight frame (NTF) approximation exists and is unique. Therefore it applies to Gabor frames (including Gabor frames for subspaces) and frames induced by translation groups. Similar results hold for semi-orthogonal wavelet frames.
Transactions of the American Mathematical Society
Number of Pages
Source API URL
Han, Deguang, "Approximations For Gabor And Wavelet Frames" (2003). Scopus Export 2000s. 1652.