On double-resolution imaging in discrete tomography

Super-resolution imaging aims at improving the resolution of an image by enhancing it with other images or data that might have been acquired using different imaging techniques or modalities. In this paper we consider the task of doubling the resolution of tomographic grayscale images of binary objects by fusion with double-resolution tomographic data that has been acquired from two viewing angles. We show that this task is polynomial-time solvable if the gray levels have been reliably determined. The task becomes NP-hard if the gray levels of some pixels come with an error of ±1 or larger. The NP-hardness persists for any larger resolution enhancement factor. This means that noise does not only affect the quality of a reconstructed image but, less expectedly, also the algorithmic tractability of the inverse problem itself.