Well-posedness of a nonlinear integro-differential problem and its rearranged formulation
This work addresses theoretical and computational challenges in nonlinear integro-differential problems for image processing applications, presenting an incremental improvement through reformulation and numerical implementation.
The authors tackled the existence and uniqueness of solutions for a nonlinear integro-differential problem by reformulating it using the decreasing rearrangement of the solution, leading to dimensional reduction and a fast numerical method. They demonstrated the model's performance in image processing tasks like filtering and segmentation.
We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained and a detailed analysis of the properties of the solutions of the model is provided. Finally, a fast numerical method is devised and implemented to show the performance of the model when typical image processing tasks such as filtering and segmentation are performed.