# Postprocessing

This is work in progress. Currently, the following functions are implemented.

`total_variation_denoising(source::AbstractVector, λ::Number)`

Compute the solution of the total variation regularized least square problem$$\\min_x \\frac{1}{2} \\sum_{k} |y_k - x_k|^2 + \\lambda \\sum_{k} |x_{k+1} - x_{k}|$$ using the explicit algorithm of Condat (2013) A Direct Algorithm for 1-D Total Variation Denoising. An inplace version`total_variation_denoising!(dest::AbstractVector, source::AbstractVector, λ::Number)`

is also provided.-
`group_sparse_total_variation_denoising(y::AbstractVector, λ::Number; group_size::Integer=1, max_iter::Integer=100)`

Compute`max_iter`

iterations of the algorithm described by Selesnick and Chen (2013) Total variation denoising with overlapping group sparsity. -
`fourier_pade(u, degree_num, degree_den, num_output=length(u))`

Compute the Fourier-Padé reconstruction of`u`

with degrees`(degree_num, degree_den)`

and evaluate it at`num_output`

equispaced points, cf. Driscoll and Fornberg (2001) A Padé-based algorithm for overcoming the Gibbs phenomenon.