tailieunhanh - Báo cáo hóa học: "Characterization of Oblique Dual Frame Pairs"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Characterization of Oblique Dual Frame Pairs | Hindawi Publishing Corporation EURASIP Journal on Applied Signal Processing Volume 2006 Article ID 92674 Pages 1-11 DOI ASP 2006 92674 Characterization of Oblique Dual Frame Pairs Yonina C. Eldar1 and Ole Christensen2 1 Department of Electrical Engineering Technion - Israel Institute of Technology Technion City Haifa 32000 Israel 2 Department of Mathematics Technical University of Denmark Building DK-303 2800 Kongens Lyngby Denmark Received 2 September 2004 Revised 17 December 2004 Accepted 21 January 2005 Given a frame for a subspace W of a Hilbert space H we consider all possible families of oblique dual frame vectors on an appropriately chosen subspace V. In place of the standard description which involves computing the pseudoinverse of the frame operator we develop an alternative characterization which in some cases can be computationally more efficient. We first treat the case of a general frame on an arbitrary Hilbert space and then specialize the results to shift-invariant frames with multiple generators. In particular we present explicit versions of our general conditions for the case of shift-invariant spaces with a single generator. The theory is also adapted to the standard frame setting in which the original and dual frames are defined on the same space. Copyright 2006 Hindawi Publishing Corporation. All rights reserved. 1. INTRODUCTION Frames are generalizations of bases which lead to redundant signal expansions 1-4 . A frame for a Hilbert space is a set of not necessarily linearly independent vectors that has the property that each vector in the space can be expanded in terms of these vectors. Frames were first introduced by Duffin and Schaeffer 1 in the context of nonharmonic Fourier series and play an important role in the theory of nonuniform sampling 1 2 5 6 . Recent interest in frames has been motivated in part by their utility in analyzing wavelet expansions 7 8 and by their robustness properties 3 813 . Frame-like expansions have been .