Parameter learning and fractional differential operators: application in image regularization and decomposition

Understand

In this paper, we focus on learning optimal parameters for PDE-based image regularization and decomposition.

• First we learn the regularization parameter and the differential operator for gray-scale image denoising using the fractional Laplacian in combination with a bilevel optimization problem.
• In our setting the fractional Laplacian allows the use of Fourier transform, which enables the optimization of the denoising operator.
• We prove stable and explainable results as an advantage in comparison to other machine learning approaches.