Detection of damage in a single tow ceramic matrix composite specimen has been achieved using orthogonal decomposition of volumetric tomographic datasets collected at four tensile loads. This decomposition approach has been applied at two different length scales: (i) individual fibres and (ii) bulk volumes containing fibres and matrix material. Volumes were first decomposed to feature vectors, orders of magnitude smaller than the original volume they describe, and then comparisons between datasets at different load levels were made in feature vector space. The results show quantitative measurements of damage location, damage morphology and the relative growth of this damage with increased load when compared with a dataset with less or no damage. No prior knowledge of the dataset or training of algorithms is required for damage to be detected, it is only necessary that at least two datasets are available for comparison, e.g. from in situ or repeated scanning measurements. Results are generated on significantly shorter timescales when compared with previous automated approaches to tomography data processing. This approach has the potential to be applied to damage detection in a range of materials through comparisons of volumetric datasets from a range of measurement or computational techniques.