The most unique advantage of multipass synthetic aperture radar interferometry (InSAR) is the retrieval of long-term geophysical parameters, e.g., linear deformation rates, over large areas. Recently, an object-based multipass InSAR framework has been proposed by Kang, as an alternative to the typical single-pixel methods, e.g., persistent scatterer interferometry (PSI), or pixel-cluster-based methods, e.g., SqueeSAR. This enables the exploitation of inherent properties of InSAR phase stacks on an object level. As a follow-on, this paper investigates the inherent low rank property of such phase tensors and proposes a Robust Multipass InSAR technique via Object-based low rank tensor decomposition. We demonstrate that the filtered InSAR phase stacks can improve the accuracy of geophysical parameters estimated via conventional multipass InSAR techniques, e.g., PSI, by a factor of 10-30 in typical settings. The proposed method is particularly effective against outliers, such as pixels with unmodeled phases. These merits, in turn, can effectively reduce the number of images required for a reliable estimation. The promising performance of the proposed method is demonstrated using high-resolution TerraSAR-X image stacks.