normTVinv2
Computes the norm induced by the inner product innergrad.
Contents
Syntax
n = normTVinv2(gus,seti)
Description
n = normTVinv2(gus,seti) computes the norm on gradient gus, which is generated by the inner product innergrad.
Input Arguments
The input arguments are described in normTVinv1.html:
- gus
- seti.dim
- seti.nInv
- seti.dVinv
Output Argument
- n : result of the norm.
More About
The norm is generated by the inner product innergrad, i.e.
,
and is not (normTVinv1.html), see [1, Sec. 4.5 above eq. (59)].
normTVinv2 uses rNorm = 2, apart from that it is similar to normTVinv1.
References
- [1] Florian Bürgel, Kamil S. Kazimierski, and Armin Lechleiter. A sparsity regularization and total variation based computational framework for the inverse medium problem in scattering. Journal of Computational Physics, 339:1-30, 2017. URL: https://doi.org/10.1016/j.jcp.2017.03.011.
See Also
Code
function n = normTVinv2(gus,seti) % Old name: n = \|\nabla u\|_{TV,2} absgu = normTVinvAux(gus,seti); rNorm = 2; if seti.dim == 2 n = (sum(sum(absgu.^rNorm))*seti.dVinv).^(1/rNorm); % \|grad(u)\|_{TV,2} = \sqrt{ \sum_i,j | (grad(u))_i,j |^2 } elseif seti.dim == 3 n = (sum(sum(sum(absgu.^rNorm)))*seti.dVinv).^(1/rNorm); end end