Imaging technologies are advancing at great speed. Already, they provide simultaneous access to a several intracellular variables throughout the cell. Here, we apply standard statistical and machine learning tools to the fitting of detailed biophsyical models to imaging data, concentrating mainly on voltage-sensitive dye recordings. We extend previous findings to take the generally very noisy nature of voltage-sensitive dye recordings into account. With knowledge of the involved channels' kinetics, Sequential Monte Carlo sampling methods allow both the inference of channel densities from noisy data, and the principled, model-based smoothing of such data. Finally we show that the requirement for knowledge of the involved channels can be relaxed by introduction of a linear reparametrisation of channel kinetics in this same framework.