Face images that are captured by surveillance cameras usually have a very low resolution, which significantly limits the performance of face recognition systems. In the past, super-resolution techniques have been proposed to increase the resolution by combining information from multiple images. These techniques use super-resolution as a preprocessing step to obtain a high-resolution image that is later passed to a face recognition system. Considering that most state-of-the-art face recognition systems use an initial dimensionality reduction method, we propose to transfer the super-resolution reconstruction from pixel domain to a lower dimensional face space. Such an approach has the advantage of a significant decrease in the computational complexity of the super-resolution reconstruction. The reconstruction algorithm no longer tries to obtain a visually improved high-quality image, but instead constructs the information required by the recognition system directly in the low dimensional domain without any unnecessary overhead. In addition, we show that face-space super-resolution is more robust to registration errors and noise than pixel-domain super-resolution because of the addition of model-based constraints.