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We present SkyFACT (Sky Factorization with Adaptive Constrained Templates), anew approach for studying, modeling and decomposing diffuse gamma-ray emission.Like most previous analyses, the approach relies on predictions from cosmic-raypropagation codes like GALPROP and DRAGON. However, in contrast to previousapproaches, we account for the fact that models are not perfect and allow for avery large number ($\gtrsim10^5$) of nuisance parameters to parameterize theseimperfections. We combine methods of image reconstruction and adaptivespatio-spectral template regression in one coherent hybrid approach. To thisend, we use penalized Poisson likelihood regression, with regularizationfunctions that are motivated by the maximum entropy method. We introducemethods to efficiently handle the high dimensionality of the convexoptimization problem as well as the associated semi-sparse covariance matrix,using the L-BFGS-B algorithm and Cholesky factorization. We test the methodboth on synthetic data as well as on gamma-ray emission from the inner Galaxy,$|\ell|<90^\circ$ and $|b|<20^\circ$, as observed by the Fermi Large AreaTelescope. We finally define a simple reference model that removes most of theresidual emission from the inner Galaxy, based on conventional diffuse emissioncomponents as well as components for the Fermi bubbles, the Fermi Galacticcenter excess, and extended sources along the Galactic disk. Variants of thisreference model can serve as basis for future studies of diffuse emission inand outside the Galactic disk.

SkyFACT: High-dimensional modeling of gamma-ray emission with adaptive templates and penalized likelihoods