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Try dragging & dropping your own images into the window!

Click into the image to change the mask.

This page demonstrates how to use variational Rudin-Osher-Fatemi method for removing noise from images. The image shows the function $u:\Omega \to \mathbb{R}$ that minimizes the energy
$$\frac{1}{2} \int_\Omega \|u(x) - f(x)\|_2^2 d x + \lambda \int \| D u (x) \|.$$
The right-hand side is also called the *Total Variation* of the image $u$.

The animation shows the intermediate steps when using a primal-dual method to solve the discretized energy.

**Authors:** Jan Lellmann, lellmann@mic.uni-luebeck.de

- Use the controls on the left to change the regularization strength $\lambda$.
- Click or tap to remove parts from the data term.
- Enable "invert" to invert the mask and click or tap to add back parts of the image.

- L. Rudin, S. Osher, E. Fatemi: Nonlinear total variation based noise removal algorithms. Physica D.: Nonlinear Phenomena, 60(1-4), pp 259-268, 1992.
- A. Chambolle, T. Pock: A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging J. Math. Imaging and Vision, 40(1), pp 120-145, 2011.