normroi
Computes the norm of a vector on the region of interest.
Contents
Syntax
n = normroi(x,seti,q) n = normroi(x,seti)
Description
- normroi(x,seti,q) computes the norm of the complex vector x on the region of interest. The norm is a q-Norm with weight seti.dV.
- normroi(x,seti) computes the norm of the complex vector x on the region of interest. The norm is a seti.qNorm-Norm with weight seti.dV.
Input Arguments
- x, y : two complex vectors of size seti.nROI^seti.dim (values in region of interest written as a vector).
- seti.dV : area/volume of the infinitesimal element (pixel/voxel) of CD, setGrid.html.
- seti.qNorm : seti.qNorm-Norm
- q : q-Norm (third argument is not necessary, if seti.qNorm was defined).
Output Arguments
- n : evaluated norm
More About
- In case of seti.qNorm = 2 or q = 2, the norm is the same as the norm induced by the inner product innerroi.html.
- The norm is defined as, see [1, Sec. 3.6],
for
with and
.
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 = normroi(x,seti,q) if nargin == 2 Q = seti.qNorm; elseif nargin == 3 Q = q; end dV = seti.dV; if Q == 2 n = sqrt(abs(innerroi(x,x,seti))); else n = norm(x(:),Q)*dV^(1/Q); % in case Q = 2 the result is the same as above end end