This paper describes an approach to analyze ground deformation data collected by InSAR (Interferometric Synthetic Aperture Radar) imaging the volcano feeding system (VFS) beneath a caldera. The approach is applied to the Campi Flegrei caldera in southern Italy, a densely populated area at high risk for volcanic eruption. The method is a 4D tomographic inversion that considers a combination of 3D pressure sources and dislocations (strike-slip, dip-slip and tensile) acting simultaneously. This is in contrast to traditional methods that assume a priori geometries and type for the volcanic source. Another novelty is that we carry out a time-series analysis of multifrequency InSAR displacement data. The analysis of these multiplatform and multifrequency InSAR data from 2011 to 2022 reveals an inflating source at a depth of 3–4 km that is interpreted as a pressurized magmatic intrusion. The source broadens and migrates laterally over time, with a possible new magmatic pulse arriving in 2018–2020. The model also identifies a shallow region (at 400 m depth) that may be feeding fumaroles in the area. The analysis also reveals a zone of weakness (dip-slip) that could influence the path of rising magma. This method provides a more detailed dynamic 4 - dimensional image of the VFS than previously possible and could be used to improve hazard assessments in active volcanic areas.