A Minimum Acceleration Approach for the Retrieval of Multiplatform InSAR Deformation Time Series

We present in this paper a technique for the generation of 3-D (2-D) displacement time series of the earth's surface, based on the combination of multiplatform SAR data. The algorithm assumes the availability of two (or more) archives of SAR images acquired from complementary (i.e., ascending/descending) tracks over the same area on the ground. SAR data are preprocessed through one of the currently available multitemporal differential interferometry synthetic aperture radar (DInSAR) toolboxes in order to recover, in correspondence to a set of very coherent points, the line-of-sight (LOS) displacement time series. The latter are then geocoded to a common grid and jointly inverted (pixel-by-pixel) to estimate the (unknown) time series of the 3-D (East-West, North-South, Up-Down) displacement components. To this aim, an underdetermined system of linear equations has to be solved. Previous works have proposed to solve similar ill-posed problems by applying the (truncated) singular-value-decomposition method and/or by regularizing the germane system of linear equations by adding further constraints, which impose conditions on the minimum-norm velocity of the solution. On the contrary, in this study, we adopt a different strategy, which is based on imposing that the 3-D deformation time series have minimum acceleration. The developed combination technique is a postprocessing tool that can be easily implemented. Indeed, it does not require the simultaneous processing of very large sequences of DInSAR interferograms. As a matter of fact, the retrieval of preliminary LOS-projected DInSAR time series can be independently carried out by using one (or more) of the currently available multitemporal DInSAR toolboxes, with no restrictions at all on the class to which they belong (small-baseline-and/or permanent-scatterers-oriented). Experiments carried out on simulated and real data prove the validity of the proposed combination algorithm in retrieving 2-D (East-West, Up-Down) surface displacement time series with sub-centimeter accuracy, and the North-South components with an accuracy of some centimeters.