Statistical-Cost, Network-Flow Algorithm for 2D Phase Unwrapping


Two-dimensional phase unwrapping is the process of recovering unambiguous phase data from a 2-D array of phase values known only modulo 2pi rad.

There are many applications, like Magnetic Resonance Imaging (MRI), Synthetic Aperture Radar (SAR), fringe pattern analysis, tomography and spectroscopy, which as part of their fundamental operation depend upon the extraction of a phase signal from their input image. Usually the phase is available in a form that suffers from 2-pi phase jumps due to the use of the mathematical arctangent function, which produces an inherently wrapped output. This wrapped phase is unusable until the phase discontinuities are removed.

SNAPHU is an implementation of the Statistical-cost, Network-flow Algorithm for Phase Unwrapping particularly suitable for SAR interferometry applications. This algorithm poses phase unwrapping as a maximum a posteriori probability (MAP) estimation problem, the objective of which is to compute the most likely unwrapped solution given the observable input data. Because the statistics relating the input data to the solution depend on the measured quantity, SNAPHU incorporates three built-in statistical models, for topography data, deformation data, and smooth generic data. The posed optimization problem is solved approximately with use of network-flow techniques.

As SNAPHU uses an iterative optimization procedure, its execution time depends on the difficulty of the interferogram. In single-tile mode the required memory is on the order of 100 MB per 1000000 pixels in the input interferogram.

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