Quarter sampling is a novel sensor concept that enables the acquisition of higher resolution images without increasing the number of pixels. This is achieved by covering three quarters of each pixel of a low-resolution sensor such that only one quadrant of the sensor area of each pixel is sensitive to light. By randomly masking different parts, effectively a non-regular sampling of a higher resolution image is performed. Combining a properly designed mask and a high-quality reconstruction algorithm, a higher image quality can be achieved than using a low-resolution sensor and subsequent upsampling. For the latter case, the image quality can be enhanced using super resolution algorithms. Recently, algorithms based on machine learning such as the Very Deep Super Resolution network (VDSR) proofed to be successful for this task. In this work, we transfer the concepts of VDSR to the special case of quarter sampling. Besides adapting the network layout to take advantage of the case of quarter sampling, we introduce a novel data augmentation technique enabled by quarter sampling. Altogether, using the quarter sampling sensor, the image quality in terms of PSNR can be increased by +0.67 dB for the Urban 100 dataset compared to using a low-resolution sensor with VDSR.