$ \DeclareMathOperator{\arccosh}{arccosh} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator{\Exp}{Exp} \newcommand{\geo}[2]{\gamma_{\overset{\frown}{#1,#2}}} \newcommand{\geoS}{\gamma} \newcommand{\geoD}[2]{\gamma_} \newcommand{\geoL}[2]{\gamma(#2; #1)} \newcommand{\gradM}{\nabla_{\M}} \newcommand{\gradMComp}[1]{\nabla_{\M,#1}} \newcommand{\Grid}{\mathcal G} \DeclareMathOperator{\Log}{Log} \newcommand{\M}{\mathcal M} \newcommand{\N}{\mathcal N} \newcommand{\mat}[1]{\mathbf{#1}} \DeclareMathOperator{\prox}{prox} \newcommand{\PT}[3]{\mathrm{PT}_{#1\to#2}#3} \newcommand{\R}{\mathbb R} \newcommand{\SPD}[1]{\mathcal{P}(#1)} \DeclareMathOperator{\Tr}{Tr} \newcommand{\tT}{\mathrm{T}} \newcommand{\vect}[1]{\mathbf{#1}} $

List of functionals

The second order mid point model functional
1
%  gradientSecondOrderLog(M,f,alpha,beta) the l^2-TV-TV2 mid point model

Computes the second order mid point model

for manifold-valued data , where is some given data, that might only be given on a subset of the domain. Then the data term is reduced accordingly.

more
The total variation prior
1
% TV(M,x) compute all TV with a p-norm coupling of forward distance terms.

Computes the total variation prior with -norm coupling of a -valued data set , where the pixel grid is of size , .

more
The second order total variation prior from the mid point prior
1
% proxTV(M,x,lambda) compute the second order TV mid point model value

Computes the total variation of second order from the mid point model. An absolute difference of second order for three points is modeled as the distance of to the nearest mid point of the geodesics connecting and .

more

See also