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- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-008-9419-8
- Publisher site
- See Article on Publisher Site
Abstract
We demonstrate that for all linear devices and/or sensors, signal requisition and reconstruction is naturally a mathematical frame expansion and reconstruction issue, whereas the measurement is carried out via a sequence generated by the exact physical response function (PRF) of the device, termed sensory frame {h n }. The signal reconstruction, on the other hand, will be carried out using the dual frame $\{\tilde{h}^{a}_{n}\}$ of an estimated sensory frame {h n a }. This consequently results in a one-sided perturbation to a frame expansion, which resides in each and every signal and image reconstruction problem. We show that the stability of such a one-sided frame perturbation exits. Examples of image reconstructions in de-blurring are demonstrated.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Feb 17, 2009