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Radar interferometry (InSAR) deformation measurements are afflicted by artifacts associated with the atmosphere and errors in removing the topographic phase contribution. We present a new time series algorithm that eliminates high-spatial-frequency atmospheric effects (bubbles) not removed with existing advanced InSAR approaches applied to measurements of smoothly varying deformation through time. Our High-Resolution Atmospheric Phase Screen (APS) (HiRAPS) algorithm initially uses a connected set of short-period interferograms, each spanning no more than three satellite-orbit repeat cycles. We estimate height error differences between a pixel and its neighbors within a radius chosen to be significantly smaller than a bubble. The height errors are unwrapped and removed from those pixels with high values of a newly defined multi-interferogram phase correlation. We then create a deformation time series for the pixels using singular value decomposition. The high-resolution APS are estimated from a dense set of pixels using spatiotemporal filtering. We evaluate the HiRAPS algorithm on simulated data consisting of realistic time-linear and nonlinear deformation, height errors, and bubbles. The root mean square error between all simulated and estimated APS pixels is 0.26 rad with the HiRAPS algorithm and 0.39 rad with a persistent scatterer (PS) algorithm. We also apply the HiRAPS algorithm to 66 Radarsat-1 images of Phoenix, AZ. Our HiRAPS approach results in an 18-fold increase in APS pixel density over PS processing. After removing the HiRAPS and PS APS from PS interferograms, we find that HiRAPS provides an 18% increase in the number of final PS detected.