We describe a new technique to constrain time-dependent deformation from repeated satellite-based InSAR observations of a given region. This approach, which we call MInTS (Multiscale analysis of InSAR Time Series), relies on a spatial wavelet decomposition to permit the inclusion of distance based spatial correlations in the observations while maintaining computational tractability. This approach also permits a consistent treatment of all data independent of the presence of localized holes in any given interferogram. In essence, MInTS allows one to considers all data at the same time (as opposed to one pixel at a time), thereby taking advantage of both spatial and temporal characteristics of the deformation field. In terms of the temporal representation, we have the flexibility to explicitly parametrize known processes that are expected to contribute to a given set of observations (e.g., co-seismic steps and post-seismic transients, secular variations, seasonal oscillations, etc.). Our approach also allows for the temporal parametrization to includes a set of general functions (e.g., splines) in order to account for unexpected processes. We allow for various forms of model regularization using a cross-validation approach to select penalty parameters. The multiscale analysis allows us to consider various contributions (e.g., orbit errors) that may affect specific scales but not others. The methods described here are all embarrassingly parallel and suitable for implementation on a cluster computer. We demonstrate the use of MInTS using a large suite of ERS-1/2 and Envisat interferograms for Long Valley Caldera, and validate our results by comparing with ground-based observations.