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I present a multitemporal algorithm with an improved filtering scheme compared with earlier works that combines and inverts a large set of unwrapped interferograms to generate an accurate time series of the surface motion. This method statistically analyzes the interferometric phase noise to identify stable pixels. Then, it applies an iterative 2-D sparse phase unwrapping operator and low-pass filter to each interferogram to obtain reliable absolute phase changes. Moreover, it uses a re-weighted least squares approach to robustly estimate the time series of the surface motion, which is followed by a temporal low-pass filter that reduces the effects of atmospheric delay. During various stages of the analysis, this approach applies a variety of sophisticated wavelet-based filters to estimate the interferometric phase noise and to reduce the effects of systematic and random artefacts, such as spatially correlated and temporally uncorrelated components of the atmospheric delay, and the digital elevation model and orbital errors. To demonstrate the capability of this method for accurately measuring nonlinear surface motions, I analyze a large set of SAR data acquired by the ENVISAT satellite from 2003 through 2010 over the south flank of the Kilauea volcano, Hawaii. The validation test shows that my approach is able to retrieve the surface displacement with an average accuracy of 6.5 mm.