Published on Fri May 28 2021

On Hamilton-Jacobi PDEs and image denoising models with certain non-additive noise

Jérôme Darbon, Tingwei Meng, Elena Resmerita

Hamilton-Jacobi PDEs govern the solution of such optimization problems when the noise model is additive. With these connections, some non-convex models for non-additive noise can be solved by applying convex optimization algorithms.

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Abstract

We consider image denoising problems formulated as variational problems. It is known that Hamilton-Jacobi PDEs govern the solution of such optimization problems when the noise model is additive. In this work, we address certain non-additive noise models and show that they are also related to Hamilton-Jacobi PDEs. These findings allow us to establish new connections between additive and non-additive noise imaging models. With these connections, some non-convex models for non-additive noise can be solved by applying convex optimization algorithms to the equivalent convex models for additive noise. Several numerical results are provided for denoising problems with Poisson noise or multiplicative noise.