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TV restoration -- Finding the optimal parameters γ and λ in Image Deblurring and Denoising (2014)
Software for Computing the optimal γ and λ for TV deblurring
Ke Chen, Elena L Piccolomini and Fabiana Zama (2014),
``An automatic regularization parameter selection algorithm in the total variation model for image deblurring",
J. Numer. Algorithms,, Vol 67 (1), pp.73-92, 2014. See PDF file.

See the left image for an example with Gaussian noise and its optimal restoration result by the method. (Note: the code works without knowing the true I of course, but PSNR can be shown for a test image I.)