  We analyze the 6.5yr all-sky data from the Fermi LAT restricted to gamma-ray
photons with energies between 0.6-307.2GeV. Raw count maps show a superposition
of diffuse and point-like emission structures and are subject to shot noise and
instrumental artifacts. Using the D3PO inference algorithm, we model the
observed photon counts as the sum of a diffuse and a point-like photon flux,
convolved with the instrumental beam and subject to Poissonian shot noise. D3PO
performs a Bayesian inference in this setting without the use of spatial or
spectral templates;i.e., it removes the shot noise, deconvolves the
instrumental response, and yields estimates for the two flux components
separately. The non-parametric reconstruction uncovers the morphology of the
diffuse photon flux up to several hundred GeV. We present an all-sky spectral
index map for the diffuse component. We show that the diffuse gamma-ray flux
can be described phenomenologically by only two distinct components: a soft
component, presumably dominated by hadronic processes, tracing the dense, cold
interstellar medium and a hard component, presumably dominated by leptonic
interactions, following the hot and dilute medium and outflows such as the
Fermi bubbles. A comparison of the soft component with the Galactic dust
emission indicates that the dust-to-soft-gamma ratio in the interstellar medium
decreases with latitude. The spectrally hard component exists in a thick
Galactic disk and tends to flow out of the Galaxy at some locations.
Furthermore, we find the angular power spectrum of the diffuse flux to roughly
follow a power law with an index of 2.47 on large scales, independent of
energy. Our first catalog of source candidates includes 3106 candidates of
which we associate 1381(1897) with known sources from the 2nd(3rd) Fermi
catalog. We observe gamma-ray emission in the direction of a few galaxy
clusters hosting radio halos.
