Mapping Air Pollution eMissions (MAPM) is a 2-year project whose goal is to develop a method to infer particulate matter (PM) emissions maps from in situ PM concentration measurements. Central to the functionality of MAPM is an inverse model. The input of the inverse model includes a spatially distributed prior emissions estimate and PM measurement time series from instruments distributed across the desired domain. In this proof-of-concept study, we describe the construction of this inverse model, the mathematics underlying the retrieval of the resultant posterior PM emissions maps, the way in which uncertainties are traced through the MAPM processing chain, and plans for future developments. To demonstrate the capability of the inverse model developed for MAPM, we use the PM.sub.2.5 measurements obtained during a dedicated winter field campaign in Christchurch, New Zealand, in 2019 to infer PM.sub.2.5 emissions maps on a city scale. The results indicate a systematic overestimation in the prior emissions for Christchurch of at least 40 %-60 %, which is consistent with some of the underlying assumptions used in the composition of the bottom-up emissions map used as the prior, highlighting the uncertainties in bottom-up approaches for estimating PM.sub.2.5 emissions maps.