A new PDE learning model for image denoising

Selecting appropriate terms to design partial differential equations (PDEs) for specific processing and vision tasks have a prominent role in achieving acceptable results. In this paper, we present an automatic method to obtain a set of suitable terms of PDE for specific processing and vision tasks. Therefore, a new optimization framework has been constructed which is constrained with PDEs in the form of linear combinations of differential terms with time-independent coefficients, and is solved through training data. The optimization problem could be solved by translating it to a least square problem through the assumption of independency of time. By this assumption, it is possible to select any arbitrary term for the PDE and blend different PDEs for processing tasks, including image denoising. Several numerical experiments in image denoising prove the present model robust to the size of data and the kind of its noise.