Enhancing Compton telescope imaging with maximum a posteriori estimation: a modified Richardson-Lucy algorithm for the Compton Spectrometer and Imager

We present a modified Richardson-Lucy (RL) algorithm tailored for image reconstruction in MeV gamma-ray observations, focusing on its application to the upcoming Compton Spectrometer and Imager (COSI) mission. Our method addresses key challenges in MeV gamma-ray astronomy by incorporating Bayesian priors for sparseness and smoothness while optimizing background components simultaneously. We introduce a novel sparsity term suitable for Poisson-sampled data in addition to a smoothness prior, allowing for flexible reconstruction of both point sources and extended emission. The performance of the algorithm is evaluated using simulated three-month COSI observations of gamma-ray lines of $^{44}$Ti (1.157 MeV), $^{26}$Al (1.809 MeV), and positron annihilation (0.511 MeV), respectively, representing various spatial features. Our results demonstrate significant improvements over conventional RL methods, particularly in suppressing artificial structures in point source reconstructions and retaining diffuse spatial structures. This work represents an important step towards establishing a robust data analysis for studying nucleosynthesis, positron annihilation, and other high-energy phenomena in our Galaxy.