Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space
HM Liu, Y Tian - Journal of Mathematics, 2024 - Wiley Online Library
Due to its potential applications in image restoration and deep convolutional neural
networks, the study of irregular frames has interested some researchers. This paper …
networks, the study of irregular frames has interested some researchers. This paper …
Discrete Gabor frames and K-discrete Gabor frames
Y Tian, W Zhang, HF Jia - Annals of Functional Analysis, 2023 - Springer
The theory of discrete Gabor (DG) frames has attracted many mathematicians and engineers
due to its potential applications in digital signal processing. As a generalization of the …
due to its potential applications in digital signal processing. As a generalization of the …
Partial Gabor frames and dual frames
Y Tian, HF Jia, GL He - International Journal of Wavelets …, 2022 - World Scientific
The theory of Gabor frames has been extensively investigated. This paper addresses partial
Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame …
Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame …
Linear independence of a finite set of time-frequency shifts
D Li - Frontiers of Mathematics in China, 2022 - Springer
This paper introduces an open conjecture in time-frequency analysis on the linear
independence of a finite set of time-frequency shifts of a given L 2 function. Firstly …
independence of a finite set of time-frequency shifts of a given L 2 function. Firstly …
Irregular wavelet/Gabor frames in Sobolev space
Y Tian - Authorea Preprints, 2022 - authorea.com
The theory of regular wavelet/Gabor frames has been extensively investigated, including the
sufficient and necessary conditions for regular wavelet/Gabor systems to be frames and the …
sufficient and necessary conditions for regular wavelet/Gabor systems to be frames and the …