Denoising three-dimensional and colored images using a Bayesian multi-scale model for photon counts

• We propose a model based Bayesian method for processing low-intensity three dimensional or colored images.
• We use a multi-scale representation of the model and process the image data in blocks of differing sizes.
• We use a novel prior that allows ties among relative intensity parameters thus encouraging formation of structures.

X-ray images of distant stars and galaxies are typically registered by low photon counts at the pixel level, for which the Poisson distribution is a sensible model description. The resulting count data can be represented in a multi-scale framework, where the likelihood function factorizes in functions of relative intensity parameters corresponding to different levels from the whole frame down to the pixel level. In a Bayesian approach, a prior is assigned on these relative intensity parameters independently across levels and the image is reconstructed using the posterior mean of intensity parameter of each pixel. A novel prior which allows ties in the values of relative intensity parameters of neighboring regions has been recently shown to be very successful in finding structures in images. We extend this idea to reconstruct colored images from noisy data. The proposed method is completely data-driven, since all smoothing parameters are automatically estimated from the data without any additional user input. In the context of astronomical X-ray images, color represents the energy level of photons, which are also typically recorded by telescopes. The energy level can be considered as the third dimension of images. In a more general sense, the technique we develop applies to all three dimensional images, and can be used to process medical images as well.