Please use this identifier to cite or link to this item:
|Title:||Convolution, average sampling, and a calderon resolution of the identity for shift-invariant spaces||Authors:||Aldroubi, A.
|Issue Date:||Apr-2005||Citation:||Aldroubi, A., Sun, Q., Tang, W.-S. (2005-04). Convolution, average sampling, and a calderon resolution of the identity for shift-invariant spaces. Journal of Fourier Analysis and Applications 11 (2) : 215-244. ScholarBank@NUS Repository. https://doi.org/10.1007/s00041-005-4003-3||Abstract:||In this article, we study three interconnected inverse problems in shift invariant spaces: 1) the convolution/deconvolution problem; 2) the uniformly sampled convolution and the reconstruction problem; 3) the sampled convolution followed by sampling on irregular grid and the reconstruction problem. In all three cases, we study both the stable reconstruction as well as ill-posed reconstruction problems. We characterize the convolutors for stable deconvolution as well as those giving rise to ill-posed deconvolution. We also characterize the convolutors that allow stable reconstruction as well as those giving rise to ill-posed reconstruction from uniform sampling. The connection between stable deconvolution, and stable reconstruction from samples after convolution is subtle, as will be demonstrated by several examples and theorems that relate the two problems. © 2005 Birkhäuser Boston. All rights reserved.||Source Title:||Journal of Fourier Analysis and Applications||URI:||http://scholarbank.nus.edu.sg/handle/10635/103077||ISSN:||10695869||DOI:||10.1007/s00041-005-4003-3|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Aug 20, 2019
WEB OF SCIENCETM
checked on Aug 12, 2019
checked on Aug 17, 2019
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.