TV/TGV denoising of image data

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

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)

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.

Details

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

Value

TV/TGV reconstructed image data (2D array)

References

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.

Author

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