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Zbl 0780.49028
Rudin, Leonid I.; Osher, Stanley; Fatemi, Emad
Nonlinear total variation based noise removal algorithms.
(English)
[J] Physica D 60, No.1-4, 259-268 (1992). ISSN 0167-2789

Summary: A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the gradient-projection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As $t\to\infty$ the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear to be state-of-the-art for very noisy images. The method is noninvasive, yielding sharp edges in the image. The technique could be interpreted as a first step of moving each level set of the image normal to itself with velocity equal to the curvature of the level set divided by the magnitude of the gradient of the image, and a second step which projects the image back onto the constraint set.
MSC 2000:
*49N70 Differential games
49N75 Pursuit and evasion games
68U10 Image processing

Keywords: noise removal; image transmission; constrained optimization; Lagrange multipliers

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