Compressed sensing (CS) represents an efficient framework to simultaneously acquire and compress images/signals while reducing acquisition time and memory requirements to process or transmit them. Specifically, CS is able to recover an image from random measurements. Recently, deep neural networks (DNNs) are exploited not only to acquire and compress but also for recovering signals/images from a highly incomplete set of measurements. Super-resolution (SR) algorithms attempt to generate a single high resolution (HR) image from one or more low resolution (LR) images of the same scene. Despite the success of the existing SR networks to recover HR images with better visual quality, there are still some challenges that need to be addressed. This paper designs a deep neural network that generates HR images from LR Xray COVID-19 images. To address this problem, we propose a novel robust deep CS framework that is able to mitigate the geometric transformation and recover HR images. Specifically, the proposed framework is able to perform two tasks. First, it is able to compress the transformed image with the help of an optimized generated measurement matrix. Second, the proposed framework is able not only to recover the original image from the compressed version but also to mitigate the transformation effects. The simulation results reported in this article show that the proposed framework is able to achieve a high level of robustness against different geometric transformations in terms of peak signal-to- noise ratio (PSNR) and similar structure index measurements (SSIM).