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.