Performance evaluation of two-dimensional phase unwrapping algorithms

We present a performance evaluation of eight two-dimensional phase unwrapping methods with respect to correct phase unwrapping and execution times. The evaluated methods are block least squares (BLS), adaptive integration (AI), quality guided path following (QUAL), mask cut (MCUT), multigrid (MGRID), preconditioned conjugate gradient (PCG), Flynn's (FLYNN), and Liang's (LIANG). This set included integration- (path following), least-squares-, L(1)-, and model-based methods. The methods were tested on several synthetic images, on two magnetic resonance images, and on two interferometry images. The synthetic images were designed to demonstrate different aspects of the phase unwrapping problem. To test the noise robustness of the methods, independent noise was added to the synthetic images to yield different signal-to-noise ratios. Each experiment was performed 50 times with different noise realizations to test the stability of the methods. The results of the experiments showed that the congruent minimum L(1) norm FLYNN method was best overall and the most noise robust of the methods, but it was also one of the slowest methods. The integration-based QUAL method was the only method that correctly unwrapped the two interferometry images. The least-squares-based methods (MGRID, PCG) gave worse results on average than did the integration- (or path following) based methods (BLS, AI, QUAL, MCUT) and were also slower. The model-based LIANG method was sensitive to noise and resulted in large errors for the magnetic resonance images and the interferometry images. In conclusion, for a particular application there is a trade-off between the quality of the unwrapping and the execution time when we attempt to select the most appropriate method.