Parallel advanced iterative algorithm for phase extraction with unknown phase-shifts

•Convergence issue regarding the data cropping of the state-of-the-art partial GPU implementation of AIA is discussed.•Structure of the AIA is analyzed to show that full parallelization is possible.•The fact that the time cost of the gAIA is not sensitive to the frame number is discovered and analyzed.•The gAIA is proposed which achieves 500 ×  and 10 ×  speedup comparing with the sequential implementation and the partial GPU implementation without scarifying the accuracy.•The real-time phase extraction with AIA is achieved by using a normal NVIDIA GPU.