A Data-Driven Loss Weighting Scheme Across Heterogeneous Tasks for Image Denoising

Abstract. In a variational denoising model, weight in the data fidelity term plays the role of enhancing the noise-removal capability. It is profoundly correlated with noise information while also balancing the data fidelity and regularization terms. However, assigning weight is expected to be challenging when the noise pattern is beyond independent identical Gaussian distribution, e.g., impulse noise, stripe noise, or a mixture of several patterns, etc. Furthermore, how to leverage weight to balance the data fidelity and regularization terms is even less evident. In this work, we propose a data-driven loss weighting (DLW) scheme to address these issues. Specifically, DLW trains a parameterized weight function (i.e., a neural network) that maps the noisy image to the weight. The training is achieved by a bilevel optimization framework, where the lower level problem is solving several denoising models with the same weight predicted by the weight function, and the upper level problem minimizes the distance between the restored image and the clean image. In this way, information from both the noise and the regularization can be efficiently extracted to determine the weight function. DLW also facilitates the easy implementation of a trained weight function on denoising models. Numerical results verify the remarkable performance of DLW on improving the ability of various variational denoising models to handle different complex noise. This implies that DLW has the ability to transfer the noise knowledge at the model level to heterogeneous tasks beyond the training models. We studythe generalization theory underlying DLW i, validating its intrinsic transferability.