Alpers, Andreas 
ORCID: 0000-0003-0663-6037 and Gritzmann, Peter
(2018)
ON DOUBLE-RESOLUTION IMAGING AND DISCRETE TOMOGRAPHY.
SIAM JOURNAL ON DISCRETE MATHEMATICS, 32 (2).
pp. 1369-1399.
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1701.04399v3.pdf - Author Accepted Manuscript Download (1MB) | Preview |
Abstract
Super-resolution imaging aims at improving the resolution of an image by enhancing it with other images or data that might have been acquired using different imaging techniques or modalities. In this paper we consider the task of doubling, in each dimension, the resolution of grayscale images of binary objects by fusion with double-resolution tomographic data that have been acquired from two viewing angles. We show that this task is polynomial-time solvable if the gray levels have been reliably determined. The problem becomes $\mathbb{N}\mathbb{P}$-hard if the gray levels of some pixels come with an error of $\pm1$ or larger. The $\mathbb{N}\mathbb{P}$-hardness persists for any larger resolution enhancement factor. This means that noise does not only affect the quality of a reconstructed image but, less expectedly, also the algorithmic tractability of the inverse problem itself.
| Item Type: | Article |
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| Additional Information: | 26 pages, to appear in SIAM Journal on Discrete Mathematics |
| Uncontrolled Keywords: | discrete mathematics, combinatorics, discrete tomography, superresolution, polynomial-time, algorithms, computational complexity |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 05 May 2020 10:26 |
| Last Modified: | 15 Mar 2024 16:31 |
| DOI: | 10.1137/17M1115629 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3085593 |
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