Affiliation:
1. School of Mathematics and Statistics Beijing Jiaotong University Beijing China
2. School of Information and Communication Engineering Beijing University of Technology Beijing China
Abstract
Nonstationary Gabor (NSG) frames for
allow for flexible sampling and varying window functions and have found applications in adaptive signal analysis. Recently, the first author of this paper generalized the notion of NSG frames for
to the space
of vector‐valued signals and investigated the existence of vector‐valued NSG (VVNSG) frames. In this paper, we consider the reconstruction of any functions in
from coefficients obtained from VVNSG frames. We provide different approximately dual frames of VVNSG frames and give the corresponding reconstruction error bounds. In particular, for a special class of VVNSG frames that are related to painless VVNSG frames, we show that the approximately dual frames carry the VVNSG structure, which is very important since there exist fast analysis and reconstruction algorithms for VVNSG frames. We also provide a method to construct the special class of VVNSG Bessel sequences. Finally, a constructive example is given to illustrate the theoretical results.
Funder
National Natural Science Foundation of China
Subject
General Engineering,General Mathematics