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Hydrocarbon reservoirs can be efficiently monitored with simultaneous-source seismic data sets. Because simultaneous-source acquisition reduces time and cost requirements, seismic data sets can be recorded cheaply at short regular intervals, thereby allowing for near real-time monitoring. Although, in many cases, the recorded multiplexed data can be separated into independent records, we choose to leverage the efficiency of direct imaging of such data sets. However, direct imaging with a migration algorithm introduces cross-talk artifacts and does not account for differences in acquisition geometry and relative shot-timing between surveys. To attenuate cross-talk artifacts and acquisition discrepancies between data sets, we propose a joint least-squares migration/inversion method. By incorporating spatio-temporal and sparseness constraints in our inversion algorithm, we ensure that the resulting time-lapse images are geologically plausible. Using a 2D numerical model, we show that our method can give results of comparable quality to migrated single-source data sets.