Open Access
2007 L 1 TV Computes the Flat Norm for Boundaries
Simon P. Morgan, Kevin R. Vixie
Abstr. Appl. Anal. 2007: 1-14 (2007). DOI: 10.1155/2007/45153


We show that the recently introduced L 1 TV functional can be used to explicitly compute the flat norm for codimension one boundaries. Furthermore, using L 1 TV, we also obtain the flat norm decomposition. Conversely, using the flat norm as the precise generalization of L 1 TV 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 L 1 TV functional. We illustrate the results and implications with examples and figures.


Download Citation

Simon P. Morgan. Kevin R. Vixie. " L 1 TV Computes the Flat Norm for Boundaries." Abstr. Appl. Anal. 2007 1 - 14, 2007.


Published: 2007
First available in Project Euclid: 27 February 2008

MathSciNet: MR2320805
zbMATH: 1145.49028
Digital Object Identifier: 10.1155/2007/45153

Rights: Copyright © 2007 Hindawi

Vol.2007 • 2007
Back to Top