There Are Thin Minimizers of the L1TV Functional
We show the surprising results that while the local reach of the boundary of an 𝐿1𝑇𝑉 minimizer is bounded below by 1/𝜆, the global reach can be smaller. We do this by demonstrating several example minimizing sets not equal to the union of the 1/𝜆-balls they contain.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/930978 |
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| _version_ | 1832566559168528384 |
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| author | Benjamin Van Dyke Kevin R. Vixie |
| author_facet | Benjamin Van Dyke Kevin R. Vixie |
| author_sort | Benjamin Van Dyke |
| collection | DOAJ |
| description | We show the surprising results that while the local reach of the boundary of an 𝐿1𝑇𝑉
minimizer is bounded below by 1/𝜆, the global reach can be smaller. We do this by demonstrating several example minimizing sets not equal to the union of the 1/𝜆-balls they contain. |
| format | Article |
| id | doaj-art-a07087c810ff4bd78bea8a03c8f8d994 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a07087c810ff4bd78bea8a03c8f8d9942025-02-03T01:03:49ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/930978930978There Are Thin Minimizers of the L1TV FunctionalBenjamin Van Dyke0Kevin R. Vixie1Department of Mathematics, Washington State University, Pullman, WA 99164-3113, USADepartment of Mathematics, Washington State University, Pullman, WA 99164-3113, USAWe show the surprising results that while the local reach of the boundary of an 𝐿1𝑇𝑉 minimizer is bounded below by 1/𝜆, the global reach can be smaller. We do this by demonstrating several example minimizing sets not equal to the union of the 1/𝜆-balls they contain.http://dx.doi.org/10.1155/2012/930978 |
| spellingShingle | Benjamin Van Dyke Kevin R. Vixie There Are Thin Minimizers of the L1TV Functional Abstract and Applied Analysis |
| title | There Are Thin Minimizers of the L1TV Functional |
| title_full | There Are Thin Minimizers of the L1TV Functional |
| title_fullStr | There Are Thin Minimizers of the L1TV Functional |
| title_full_unstemmed | There Are Thin Minimizers of the L1TV Functional |
| title_short | There Are Thin Minimizers of the L1TV Functional |
| title_sort | there are thin minimizers of the l1tv functional |
| url | http://dx.doi.org/10.1155/2012/930978 |
| work_keys_str_mv | AT benjaminvandyke therearethinminimizersofthel1tvfunctional AT kevinrvixie therearethinminimizersofthel1tvfunctional |