$ \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 gradients

gradient of the distance functions first argument
1
% gradDistance(M,x,y,p) gradient of f(x) = 1/p d^p(x,y)for fixed y in M.

The gradient of for a fixed value and , with standard .

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gradient of the second order TV mid point model
1
%  gradientSecondOrderLog(M,f,alpha,beta) --- compute the gradient of

For data on a -dimensional grid this function returns the gradient of the first and second order total variation additive mid point model.

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gradient of the TV prior
1
% gradTV(M,x) compute the gradient of the manifold total variation

For data on a -dimensional grid with this function comutes the gradient of the TV prior

with respect to all entries of , i.e. .

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gradient of the second order TV mid point model prior
1
% gradTV2Midpoint(M,x) compute gradient of the second order mid point model

For data on a -dimensional grid this function returns the gradient of the absolute second order total variation prior.

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See also