Super-resolution reconstruction of background-oriented Schlieren displacement field based on the convolution neural network with the gradient loss function

To refine the displacement field of the background-oriented Schlieren method, a novel super-resolution method based on deep learning has been proposed and compared with the bicubic interpolation in this study. The gradient loss functions were first introduced into the hybrid downsampled skip-connection/multi-scale model to improve the reconstruction effect. The reconstruction effects of the new loss functions were compared with that of the traditional mean square error (MSE) loss function. The results show that the Laplace operator with average pooling exhibits better performance than the origin loss function in all the indexes including peak signal-to-noise ratio, MSE, MSE of the gradient, and the maximum MSE. In these four indexes, the MSE of the gradient and the maximum MSE performed especially better than the others, where the MSE of the gradient was reduced from 3. 0× 10⁻⁰⁵ to 3.30 × 10⁻⁰⁵, and the maximum MSE was reduced from 0.392 to 0.360.