Phase Retrieval Algorithm (Python/Matlab)

Matlab/Python Implementation of simple iterative optimization phase retrieval algorithm of Fienup type (HIO/ER).

• GPU accelerating is applied under cupy with 10x speed increase , if installed.

Algorithm

Phase recovery algorithm: Input the Fourier transformed amplitude of the two-dimensional grayscale image, and achieve image reconstruction through reprojection and domain constraints without the need for phase. Phase recovery algorithms are widely used in coherent diffraction imaging, intensity interference imaging, scattering imaging and other fields.

Fienup-type phase recovery algorithms are also divided into different algorithms according to their spatial domain constraints. The more common ones are Error-Reduction (ER) and Hybrid-Input-Output (HIO) algorithms. The object space constraints of the ER algorithm are as shown in the formula, where $\gamma$ represents the prior physical constraints of the object space, that is, the image of the object space needs to be non-negative and real. Pixels that do not satisfy the physical constraint are set to zero, and pixels that satisfy the constraint are retained.

Update strategy of Error-Reduction algorithm

Update strategy of Hybrid-Input-Output algorithm

Run

Python

• Phase retrieval with HIO oversample ×1,×2 and ×4 :

  python test_phase_retrieval_oversample.py

• Benchmark of between Numpy and cupy:

  python benchmark.py

Matlab

• Run script Run_Phase_Retrieval.m in Matlab

Result

• Oversample ratio ×1, ×2 and ×4

• Run in Matlab

Link

• other vison of phase retrieval algorithm

• phase retrieval via neural network