Academic Journal
On the linear convergence rates of exchange and continuous methods for total variation minimization
| Title: | On the linear convergence rates of exchange and continuous methods for total variation minimization |
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| Authors: | Flinth, Axel, 1992, de Gournay, Frederic, Weiss, Pierre |
| Source: | Mathematical Programming. 190(1-2):221-257 |
| Subject Terms: | Inverse problems, Total variation minimization, Superresolution, Semi-infinite programming |
| Description: | We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M(Omega) of Radon measures on a subset Omega of R-d. Our main result states that under some regularity conditions, the method eventually converges linearly. Additionally, we prove that continuously optimizing the amplitudes of positions of the target measure will succeed at a linear rate with a good initialization. Finally, we propose to combine the two approaches into an alternating method and discuss the comparative advantages of this approach. |
| File Description: | electronic |
| Access URL: | https://research.chalmers.se/publication/518013 https://research.chalmers.se/publication/518013/file/518013_Fulltext.pdf |
| Database: | SwePub |
| ISSN: | 14364646 00255610 |
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| DOI: | 10.1007/s10107-020-01530-0 |