L1TV Computes the Flat Norm for Boundaries
We show that the recently introduced L1TV functional can be used to explicitly compute the flat norm for codimension one boundaries. Furthermore, using L1TV, we also obtain the flat norm decomposition. Conversely, using the flat norm as the precise generalization of L1TV functional, we obtai...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2007-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2007/45153 |
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| Summary: | We show that the recently introduced L1TV functional can be used
to explicitly compute the flat norm for codimension one boundaries.
Furthermore, using L1TV, we also obtain the flat norm
decomposition. Conversely, using the flat norm as the precise
generalization of L1TV functional, we obtain a method for
denoising nonboundary or higher codimension sets. The flat norm
decomposition of differences can made to depend on scale using the
flat norm with scale which we define in direct analogy to the
L1TV functional. We illustrate the results and implications with
examples and figures. |
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| ISSN: | 1085-3375 1687-0409 |