Phase unwrapping by means of multigrid techniques for interferometric SAR

Weighted least squares phase unwrapping is a robust approach to phase unwrapping that unwraps around (rather than through) regions of corrupted phase. Currently, the only practical method for solving the weighted least squares equations is a preconditioned conjugate gradient (PCG) technique. In this paper the authors present a new method for weighted least squares phase unwrapping. Their method is a multigrid technique that solves the equations on smaller, coarser grids by means of Gauss-Seidel relaxation schemes and transfers the intermediate results to the finer grids. A key idea of their approach is to maintain the partial derivatives of the given phase data in separate arrays and to correct these derivatives at the boundaries of the coarser grids. This correction maintains the boundary conditions necessary for convergence to the correct solution. Another key idea of their approach is to transfer the weighting values to the coarser grids in a carefully defined manner. They also present methods for defining the initial phase weights in an automated fashion. The resulting multigrid algorithm converges in only one or two multigrid cycles and is generally 15-25 times faster than the PCG technique.