document: Well-posed anisotropic diffusion for image denoising A nonlinear iterative smoothing filter based on a second-order partial differential equation is introduced . It smooths out the image according to an anisotropic diffusion process . The approach is based on a smooth approximation of the total variation -LRB- TV -RRB- functional which overcomes the non-differentiability of the TV functional at the origin . In particular , the authors perform linear smoothing over smooth areas but selective smoothing over candidate edges . By relating the smoothing parameter to the time step , they arrive at a CFL condition which guarantees the causality of the discrete scheme . This allows the adoption of higher time discretisation steps , while ensuring the absence of artefacts deriving from the non-smooth behaviour of the TV functional at the origin . In particular , it is shown that the proposed approach avoids the typical staircase effects in smooth areas which occur in the standard time-marching TV scheme
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