A parallel path-following phase unwrapping algorithm based on a top-down breadth-first search approach

Abstract Path-following methods for two-dimensional phase unwrapping such as the Goldstein algorithm are the most efficient and robust methods in remote sensing, digital phase shifting, and nuclear magnetic resonance imaging, among others. Several authors have attempted to sketch parallel versions of path-following methods. However, only the first stages of the algorithm such as residue identification and branch-cut placement have been improved using parallel architectures, with limitations such as phase maps with a single continuous region and without isolated regions owing to the cuts. In this article, a systematic parallel Goldstein algorithm that can handle phase data with multi-regions and isolated regions is proposed. Our proposal can improve the three steps of the serial Goldstein algorithm, residue identification, branch cut, and integration. In particular, the integration step is formulated as a top-down breadth-first search problem on a graph for which a parallel algorithm was developed. Synthetic and real phase maps were used to validate the performance and robustness of the proposed parallel algorithm on a multicore architecture. For simulated and real phase maps, we obtained a speedup of 3.3 and 1.98, respectively, on a laptop computer with modest hardware resources.