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

Add noise to the data, which is done by adding Gaussian noise and “wrapping” it to the $\mathbb S^n$, i.e. in $T_x\M$ of some data $x\in\M$ this function adds white Gaussian noise (componentwise) to a zero tangent vector and perform an exponential map $x_{\text{noisy}} = \exp_x(\eta)$, where $\eta$ is Gaussian noise on $\mathbb R^n$.

Matlab Documentation

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% fn = addNoise(f,sigma) add Gaussian tangential noise to f w/ deviation sigma
%
% INPUT
%   f   : data on Sn
% sigma : standard deviation
%
% OUTPUT
%  fn  : noisy data
% ---
% Manifold-Valued Image Restoration Toolbox 1.0
% R. Bergmann ~ 2018-03-03