Sensors of different wavelengths in remote sensing field capture data. Each and every sensor has its own capabilities and limitations. Synthetic aperture radar (SAR) collects data that has a high spatial and radiometric resolution. The optical remote sensors capture images with good spectral information. Fused images from these sensors will have high information when implemented with a better algorithm resulting in the proper collection of data to predict weather forecasting, soil exploration, and crop classification. This work encompasses a fusion of optical and radar data of Sentinel series satellites using a deep learning-based convolutional neural network (CNN). The three-fold work of the image fusion approach is performed in CNN as layered architecture covering the image transform in the convolutional layer, followed by the activity level measurement in the max pooling layer. Finally, the decision-making is performed in the fully connected layer. The objective of the work is to show that the proposed deep learning-based CNN fusion approach overcomes some of the difficulties in the traditional image fusion approaches. To show the performance of the CNN-based image fusion, a good number of image quality assessment metrics are analyzed. The consequences demonstrate that the integration of spatial and spectral information is numerically evident in the output image and has high robustness. Finally, the objective assessment results outperform the state-of-the-art fusion methodologies.
We refer to Krupka’s variational sequence, i.e. the quotient of the de Rham sequence on a finite order jet space with respect to a ‘variationally trivial’ subsequence. Among the morphisms of the variational sequence there are the Euler-Lagrange operator and the Helmholtz operator. In this note we show that the Lie derivative operator passes to the quotient in the variational sequence. Then we define the variational Lie derivative as an operator on the sheaves of the variational sequence. Explicit representations of this operator give us some abstract versions of Noether’s theorems, which can be interpreted in terms of conserved currents for Lagrangians and Euler-Lagrange morphisms.