Pansharpening Techniques: Optimizing the Loss Function for Convolutional Neural Networks

Pansharpening is a traditional image fusion problem where the reference image (or ground truth) is not accessible. Machine-learning-based algorithms designed for this task require an extensive optimization phase of network parameters, which must be performed using unsupervised learning techniques. The learning phase can either rely on a companion problem where ground truth is available, such as by reproducing the task at a lower scale or using a pretext task, or it can use a reference-free cost function. This study focuses on the latter approach, where performance depends not only on the accuracy of the quality measure but also on the mathematical properties of these measures, which may introduce challenges related to computational complexity and optimization. The evaluation of the most recognized no-reference image quality measures led to the proposal of a novel criterion, the Regression-based QNR (RQNR), which has not been previously used. To mitigate computational challenges, an approximate version of the relevant indices was employed, simplifying the optimization of the cost functions. The effectiveness of the proposed cost functions was validated through the reduced-resolution assessment protocol applied to a public dataset (PairMax) containing images of diverse regions of the Earth's surface.