  Inverse problems defined naturally on the sphere are becoming increasingly of
interest. In this article we provide a general framework for evaluation of
inverse problems on the sphere, with a strong emphasis on flexibility and
scalability. We consider flexibility with respect to the prior selection
(regularization), the problem definition - specifically the problem formulation
(constrained/unconstrained) and problem setting (analysis/synthesis) - and
optimization adopted to solve the problem. We discuss and quantify the
trade-offs between problem formulation and setting. Crucially, we consider the
Bayesian interpretation of the unconstrained problem which, combined with
recent developments in probability density theory, permits rapid, statistically
principled uncertainty quantification (UQ) in the spherical setting. Linearity
is exploited to significantly increase the computational efficiency of such UQ
techniques, which in some cases are shown to permit analytic solutions. We
showcase this reconstruction framework and UQ techniques on a variety of
spherical inverse problems. The code discussed throughout is provided under a
GNU general public license, in both C++ and Python.
