Methods for reconstruction of 2-D sequences from Fourier transform magnitude

Area of Science:

• Optics and Photonics
• Signal Processing
• Computational Imaging

Background:

• The Gerchberg-Saxton (GS) algorithm and its variants are standard for phase retrieval.
• Existing algorithms may fail to converge to the correct solution, even when unique solutions exist.
• Phase retrieval is crucial in various imaging and scientific applications.

Purpose of the Study:

• To propose a new deautocorrelation algorithm and auxiliary techniques to improve phase retrieval.
• To enhance the success rate and robustness of phase retrieval compared to existing methods.
• To investigate the impact of noise on reconstruction quality and explore solution ambiguity.

Main Methods:

• Development of a novel deautocorrelation algorithm.
• Integration of the new algorithm with the iterative Fourier transform (IFT) algorithm.
• Testing the combined approach on challenging reconstruction examples with varying signal-to-noise ratios (SNR).

Main Results:

• The combination of the new deautocorrelation algorithm and IFT significantly improves phase retrieval success.
• Robust and effective reconstructions were achieved even with noisy Fourier modulus data (down to 10 dB SNR).
• Perfect reconstruction is possible with noise-free data.

Conclusions:

• The proposed algorithm combination offers a more reliable approach to phase retrieval.
• The study introduces the concept of intrinsic ambiguity in phase retrieval.
• Verification of retrieved solutions is essential due to potential ambiguities and algorithm limitations.