TV_denoising: TV/TGV denoising of image data

Description

Total variation and total generalized variation are classical energy minimizing methods for image denoising.

Usage

TV_denoising(datanoisy, alpha, iter = 1000, tolmean = 1e-06,
             tolsup = 1e-04, scale = 1, verbose=FALSE)
TGV_denoising(datanoisy, alpha, beta, iter = 1000, tolmean = 1e-06,
              tolsup = 1e-04, scale = 1, verbose=FALSE)
TV_denoising_colour(datanoisy, alpha, iter = 1000, tolmean = 1e-06,
                    tolsup = 1e-04, scale = 1, verbose=FALSE)
TGV_denoising_colour(datanoisy, alpha, beta, iter = 1000, tolmean = 1e-06,
                     tolsup = 1e-04, scale = 1, verbose=FALSE)

Value

TV/TGV reconstructed image data (2D array)

Arguments

datanoisy: matrix of noisy 2D image data. In case of TV_denoising_colour and TGV_denoising_colour and array with third dimension refering to RGB channels.
alpha: TV regularization parameter.
beta: additional TGV regularization parameter.
iter: max. number of iterations
tolmean: requested accuracy for mean image correction
tolsup: requested accuracy for max (over pixel) image correction
scale: image scale
verbose: report convergence diagnostics.

Author

Joerg Polzehl, polzehl@wias-berlin.de, https://www.wias-berlin.de/people/polzehl/

Details

Reimplementation of original matlab code by Kostas Papafitsoros (WIAS).

References

J. Polzehl, K. Papafitsoros, K. Tabelow (2020). Patch-Wise Adaptive Weights Smoothing in R, Journal of Statistical Software, 95(6), 1-27. doi:10.18637/jss.v095.i06.

Rudin, L.I., Osher, S. and Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Phys. D, 60, 259-268. DOI: 10.1016/0167-2789(92)90242-F.

Bredies, K., Kunisch, K. and Pock, T. (2010). Total Generalized Variation. SIAM J. Imaging Sci., 3, 492-526. DOI:10.1137/090769521.