There is no method that will work on every dataset.
x=websave('tmp.mat','https://www.mathworks.com/matlabcentral/answers/uploaded_files/1111515/noisydata.mat');
S=load(x);
data=S.dataset;
plot(data),axis([1 numel(data) min(data) max(data)])
Should this be a sign wave?
Should it contain only discrete values?
Should it be a train of stairsteps that drop down to a baseline?
Without knowing what your data should be, it is not possible to tell which parts of your data are noise.
