We develop an algorithm for the minimum <i>L</i><sup>p</sup>-norm solution to the two-dimensional phase unwrapping problem. Rather than its being a mathematically intractable problem, we show that the governing equations are equivalent to those that describe weighted least-squares phase unwrapping. The only exception is that the weights are data dependent. In addition, we show that the minimum <i>L</i><sup>p</sup>-norm solution is obtained by embedding the transform-based methods for unweighted and weighted least squares within a simple iterative structure. The data-dependent weights are generated within the algorithm and need not be supplied explicitly by the user. Interesting and useful solutions to many phase unwrapping problems can be obtained when <i>p</i>< 2. Specifically, the minimum <i>L</i><sup>0</sup>-norm solution requires the solution phase gradients to equal the input data phase gradients in as many places as possible. This concept provides an interesting link to branch-cut unwrapping methods, where none existed previously.
© 1996 Optical Society of America
Dennis C. Ghiglia and Louis A. Romero, "Minimum Lp-norm two-dimensional phase unwrapping," J. Opt. Soc. Am. A 13, 1999-2013 (1996)