Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm.

An algorithm for unwrapping noisy phase maps by means of branch cuts has been proposed recently. These cuts join discontinuity sources that mark the beginning or end of a 2π phase discontinuity. After the placement of branch cuts, the unwrapped phase map is unique and independent of the unwrapping route. We show how a minimum-cost-matching graph-theory method can be used to find the set of cuts that has the global minimum of total cut length, in time approximately proportional to the square of the number of sources. The method enables one to unwrap unfiltered speckle-interferometry phase maps at higher source densities (0.1 sources pixel(-1)) than any previous branch-cut placement algorithm.