Solving Continuous-domain Problems Exactly with Multiresolution B-splines
| Autor: | Harshit Gupta, Thomas Debarre, Julien Fageot, Michael Unser |
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| Jazyk: | angličtina |
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| Zdroj: | ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) ICASSP |
| DOI: | 10.1109/icassp.2019.8683214 |
| Popis: | We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our method consists in restricting the search space to splines with knots on a uniform grid, which results in a standard convex finite-dimensional problem. As basis functions for this search space, we use the B-splines matched to the regularization order, which are optimally localized. This leads to a well-conditioned, computationally feasible optimization task. Our proposed iterative multiresolution algorithm then refines the grid size until a desired level of accuracy is met and converges to sparse solutions of our inverse problem. Finally, we present experimental results that validate our approach. |
| Databáze: | OpenAIRE |
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