X-ray scattering images contain numerous gaps and defects arising from detector limitations and experimental configuration. We present a method to heal X-ray scattering images, filling gaps in the data and removing defects in a physically meaningful manner. Unlike generic inpainting methods, this method is closely tuned to the expected structure of reciprocal-space data. In particular, we exploit statistical tests and symmetry analysis to identify the structure of an image; we then copy, average and interpolate measured data into gaps in a way that respects the identified structure and symmetry. Importantly, the underlying analysis methods provide useful characterization of structures present in the image, including the identification of diffuse versus sharp features, anisotropy and symmetry. The presented method leverages known characteristics of reciprocal space, enabling physically reasonable reconstruction even with large image gaps. The method will correspondingly fail for images that violate these underlying assumptions. The method assumes point symmetry and is thus applicable to small-angle X-ray scattering (SAXS) data, but only to a subset of wide-angle data. Our method succeeds in filling gaps and healing defects in experimental images, including extending data beyond the original detector borders.