Here are some simulations I did for image denoising

	This model is proposed in L. Rudin, S. Osher and E. Fatemi, "Non Linear Total Variation Based Noise Removal Algorithms", Physica D, Vol. 60, pp. 259-268, 1992
	Given the noisy image f, one tries to find the clean image u as the minimizer of the energy
	The associated Euler-Lagrange equation can be derived as
	The parameter need to be optimized. Small introduces more smoothing in u while large keep more noise in u.
	I show two examples here to demonstrate the algorithm. First I add Gaussian noise to the images and then denoise them. (left: original image , center: noisy image, right: denoised image)