To overcome the shortcomings of the existing methods for SISR, this paper presents new analytical modeling approaches. The system combines DL structures and mathematical model, where fully convolutional network for mapping between low and high-resolution images is optimized. It combines adaptive filtering mechanisms, multi-scale feature extraction block, hybrid loss that utilize both perceptual and structural similarity loss, and attention part for saliency. To measure the quality of the method, the results are compared by the peak signal-to-noise ratio, the structural similarity index, and visual quality. The lightweight architectures are developed to work in real-time applications and can learn from single channel gray scale image to multi-channel color images at the same time. The goal of the work is to increase the quality of image processing due to straightforward, efficient, and scalable single-image super-resolution techniques for particular domains or multiple uses.