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Optimizing the minimum cost flow algorithm for the phase unwrapping process in SAR radar

Dudczyk J., Kawalec A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2014

Vol. 62, nr 3

511--516

The last three decades have been abundant in various solutions to the problem of Phase Unwrapping in a SAR radar. Basically, all the existing techniques of Phase Unwrapping are based on the assumption that it is possible to determine discrete ”derivatives” of the unwrapped phase. In this case a discrete derivative of the unwrapped phase means a phase difference (phase gradient) between the adjacent pixels if the absolute value of this difference is less than π. The unwrapped phase can be reconstructed from these discrete derivatives by adding a constant multiple of 2π. These methods differ in that the above hypothesis may be false in some image points. Therefore, discrete derivatives determining the unwrapped phase will be discontinuous, which means they will not form an irrotational vector field. Methods utilising branch-cuts unwrap the phase by summing up specific discrete partial derivatives of the unwrapped phase along a path. Such an approach enables internally cohesive results to be obtained. Possible summing paths are limited by branch-cuts, which must not be intersected. These branch-cuts connect local discontinuities of discrete partial derivatives. The authors of this paper performed parametrization of the Minimum Cost Flow algorithm by changing the parameter determining the size of a tile, into which the input image is divided, and changing the extent of overlapping of two adjacent tiles. It was the basis for determining the optimum (in terms of minimum Phase Unwrapping time) performance of the Minimum Cost Flow algorithm in the aspect of those parameters.

A scaling out-of-kilter algorithm for minimum cost flow

Ciupala L.

Control and Cybernetics

2005

Vol. 34, no 4

1169-1174

The out-of-kilter algorithm is one of the basic algorithms that solve the minimum cost flow problem. Its drawback is that it can improve the objective function at each iteration by only a small value. Consequently, it runs in pseudo-polynomial time. In this paper, we describe a new out-of-kilter algorithm for minimum cost flow that runs in polynomial time. Our algorithm is a scaling algorithm and improves the objective function at each time by a "sufficiently large" value.