This paper introduces a new method called SPIIRE (Statistical Plume Imaging Inversion for Rate Estimation) to more accurately measure gas emission rates, like methane, using satellite imaging. Past methods often relied on human operators and were therefore error prone. Instead, SPIIRE uses a statistical method that matches data to a flexible plume model, enabling rate estimates for complex plumes. SPIIRE shows good performance on real data including point sources, overlapping plumes, and wide area sources like landfills.