Definition
The total variation (TV) is a nonnegative, convex, and lower semicontinuous functional on the space of integrable functions. For a function \(u\in{{\mathcal L}^1_{\text{loc}}}(\Omega)\) on a domain \(\Omega\subset{\mathbb R}{n}\), it is defined as
For differentiable functions \(u\in{\mathcal C}^1(\Omega)\), this definition can be reduced to the familiar expression
with the help of Gauss' integral theorem. A function with J(u) < ∞ is called of bounded variation; the space of all functions on Ω with bounded variation is denoted by \({{\mathcal{BV}}(\Omega)}\).
Background
The total variation is a favorite prior term and regularizer in...
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Goldluecke, B. (2014). Total Variation. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_682
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DOI: https://doi.org/10.1007/978-0-387-31439-6_682
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