Computes the total variation prior with -norm coupling of a -valued data set , where the pixel grid is of size , .
Let be the set of forward neighbors, then this function computes
where and is a relacation that is by default set to . This relacation is applied to each summand for .
- relax the TV (especially for by replacing any distance by and for each inner sum (over ) is relaxed to avoid subgradients in constant areas.
- denotes the outer coupling of the differences
weightsfor each item of
- introduces a weight that is muliplied to any term, i.e. if weights is zero this the corresponding data item is ignored.
- setting this value to
falseommits the outer sum and returns the TV value per pixel. This is used in the computation of the
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 % TV(M,x) compute all TV with a p-norm coupling of forward distance terms. % % INPUT % M : a manifold % x : data (size [manDims,dataDims]) % % OPTIONAL % 'p' : (p=1) compute TV with p-norm coupling in the dimensions of % the data, i.e. anisotropic TV for p=1 and isotropic for p=2 % 'epsilon' : compute the gradient of the epsilon-relaxed TV % 'weights' : (ones(dataDims) exclude certain data points from all % gradient terms % 'Sum' : (true) return a value (true) or a matrix of TV terms (false) % --- % MVIRT, R. Bergmann, 2017-12-08