  In this paper, we consider the problem of reconstructing a galaxy's stellar
population-kinematic distribution function from optical integral field unit
measurements. These quantities are connected via a high-dimensional integral
equation. To solve this problem, we propose a projected Nesterov-Kaczmarz
reconstruction (PNKR) method, which efficiently leverages the problem structure
and incorporates physical prior information such as smoothness and
non-negativity constraints. To test the performance of our reconstruction
approach, we apply it to a dataset simulated from a known ground truth density,
and validate it by comparing our recoveries to those obtained by the widely
used pPXF software.
