We present a generic regularized formulation, based on robust half-quadratic regularization, for unwrapping noisy and discontinuous wrapped phase maps. Two cases are presented: the convex case and the nonconvex case. The unwrapped phase with the convex formulation is unique and robust to noise; however, the convex function solution deteriorates as a result of real discontinuities in phase maps. Therefore we also present a nonconvex formulation that, with a parameter continuation strategy, shows superior performance.
© 2004 Optical Society of America
(100.2650) Image processing : Fringe analysis
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
Mariano Rivera and Jose L. Marroquin, "Half-quadratic cost functions for phase unwrapping," Opt. Lett. 29, 504-506 (2004)