Quarter sampling and three-quarter sampling are novel sensor concepts that enable the acquisition of higher resolution images without increasing the number of pixels. This is achieved by non-regularly covering parts of each pixel of a low-resolution sensor such that only one quadrant or three quadrants of the sensor area of each pixel is sensitive to light. 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 further enhanced using super resolution algorithms such as the very deep super resolution network (VDSR). In this paper, we propose a novel end-to-end neural network to reconstruct high resolution images from non-regularly sampled sensor data. The network is a concatenation of a locally fully connected reconstruction network (LFCR) and a standard VDSR network. Altogether, using a three-quarter sampling sensor with our novel neural network layout, the image quality in terms of PSNR for the Urban100 dataset can be increased by 2.96 dB compared to the state-of-the-art approach. Compared to a low-resolution sensor with VDSR, a gain of 1.11 dB is achieved.