Astronomical imaging based on photon count data is a non-trivial task. In this context we show how to denoise, deconvolve, and decompose multi-domain photon observations. The primary objective is to incorporate accurate and well motivated likelihood and prior models in order to give reliable estimates about morphologically different but superimposed photon flux components present in the data set. Thereby we denoise and deconvolve photon counts, while simultaneously decomposing them into diffuse, point-like and uninteresting background radiation fluxes. The decomposition is based on a probabilistic hierarchical Bayesian parameter model within the framework of information field theory (IFT). In contrast to its predecessor D~(3)PO, D~(4)PO reconstructs multi-domain components. Thereby each component is defined over its own direct product of multiple independent domains, for example location and energy. D~(4)PO has the capability to reconstruct correlation structures over each of the sub-domains of a component separately. Thereby the inferred correlations implicitly define the morphologically different source components, except for the spatial correlations of the point-like flux. Point-like source fluxes are spatially uncorrelated by definition. The capabilities of the algorithm are demonstrated by means of a synthetic, but realistic, mock data set, providing spectral and spatial information about each detected photon. D~(4)PO successfully denoised, deconvolved, and decomposed a photon count image into diffuse, point-like and background flux, each being functions of location as well as energy. Moreover, uncertainty estimates of the reconstructed fields as well as of their correlation structure are provided employing their posterior density function and accounting for the manifolds the domains reside on.
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