Two-dimensional (2-D) phase unwrapping, that is, deducing unambiguous phase values from a 2-D array of values known only modulo 2π, is a key step in interpreting data acquired with synthetic aperture radar interferometry. Noting the recent network formulation of the phase unwrapping problem, we apply here some well-established ideas of network theory to formalize the problem, analyze its complexity, and derive algorithms for its solution. It has been suggested that the objective of phase unwrapping should be to minimize the total number of places where unwrapped and wrapped phase gradients differ. Here we use network constructions to show that this so-called minimum $L^0$-norm problem is NP-hard, or one that complexity theory suggests is impossible for efficient algorithms to solve exactly. Therefore we must instead find approximate solutions; we present two new algorithms for doing so. The first uses the network ideas of shortest paths and spanning trees to improve on the Goldstein et al. residue-cut algorithm [Radio Sci. 23, 713 (1988)]. Our improved algorithm is very fast, provides complete coverage, and allows user-defined weights. With our second algorithm, we extend the ideas of linear network flow problems to the nonlinear $L^0$ case. This algorithm yields excellent approximations to the minimum $L^0$ norm. Using interferometric data, we demonstrate that our algorithms are highly competitive with other existing algorithms in speed and accuracy, outperforming them in the cases presented here.

Active layer thickness (ALT) is a critical parameter for monitoring the status of permafrost that is typically measured at specific locations using probing, in situ temperature sensors, or other ground-based observations. Here we evaluated the Remotely Sensed Active Layer Thickness (ReSALT) product that uses the Interferometric Synthetic Aperture Radar technique to measure seasonal surface subsidence and infer ALT around Barrow, Alaska. We compared ReSALT with ground-based ALT obtained using probing and calibrated, 500 MHz Ground Penetrating Radar at multiple sites around Barrow. ReSALT accurately reproduced observed ALT within uncertainty of the GPR and probing data in ~76% of the study area. However, ReSALT was less than observed ALT in ~22% of the study area with well-drained soils and in ~1% of the area where soils contained gravel. ReSALT was greater than observed ALT in some drained thermokarst lake basins representing ~1% of the area. These results indicate remote sensing techniques based on InSAR could be an effective way to measure and monitor ALT over large areas on the Arctic coastal plain.

Global Analysis of Titan: In its orbit around Saturn, the Cassini spacecraft passes regularly by the planet's largest moon, Titan. Using a radar instrument to peer through the moon's thick atmosphere, Zebker et al. (p. 921 , published online 2 April) developed a global model of Titan. Titan is slightly oblate, so that its poles have lower elevations than the equator, which may explain why the moon's hydrocarbon lakes are located at high latitudes.