Fast Fourier-Based Phase Unwrapping on the Graphics Processing Unit in Real-Time Imaging Applications

Numerous imaging techniques measure data that are mathematically wrapped to the finite interval [−π, π], corresponding to the principle value domain of the arctangent function. A wide range of reconstruction algorithms has been developed to obtain the true, unwrapped phase by adding an integral multiple of 2π to each point of the wrapped grid. However, the phase unwrapping procedure is hampered by the presence of noise, phase vortices or insufficiently sampled digital data. Unfortunately, reliable phase unwrapping algorithms are generally computationally intensive and their design often requires multiple iterations to reach convergence, leading to high execution times. In this paper, we present a high-speed phase unwrapping algorithm that is robust against noise and phase residues. By executing the parallel implementation of a single-step Fourier-based phase unwrapping algorithm on the graphics processing unit of a standard graphics card, we were able to reduce the total processing time of the phase unwrapping algorithm to < 5 ms when executed on a 640 × 480-pixel input map containing an arbitrarily high density of phase jumps. In addition, we expand upon this technique by inserting the obtained solution as a preconditioner in the conjugate gradient technique. This way, phase maps that contain regions of low-quality or invalid data can be unwrapped iteratively through weighting of local phase quality.