Oversampling smoothness (OSS): an effective algorithm for phase retrieval of noisy diffraction intensities

Abstract: Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free electron lasers, high harmonic generation, soft X-ray laser and electrons. Despite these rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here we present an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stage of the iterative process (i.e. a smoothness constraint), OSS finds a balance between the hybrid input-output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both our numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. We expect OSS to find application in the rapidly growing CDI field as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed.

Oversampling Smoothness for Enhanced Phase Retrieval in Coherent Diffraction Imaging

The research article presents a novel iterative algorithm named oversampling smoothness (OSS) designed to improve phase retrieval from noisy diffraction patterns. It addresses a key challenge in coherent diffraction imaging (CDI), particularly for weakly scattering biological specimens. Coherent diffraction imaging (CDI) leverages high-resolution lensless microscopy that utilizes various radiation sources such as synchrotron radiation and X-ray free electron lasers (X-FELs). Despite advances in CDI methods, reconstructing fine details from noisy data remains problematic for weakly scattering objects. The OSS algorithm introduces an innovative constraint that enhances accuracy and consistency in phase recovery, outperforming traditional approaches such as hybrid input-output (HIO), ER-HIO, and NR-HIO.

The OSS algorithm exploits the correlation in the region outside a support in real space by applying tailored spatial frequency filters, ensuring a smoother transition in reconstructions. This approach effectively reduces oscillations, mitigates the effects of Poisson noise, and balances the search between the global minima of solution space typical of HIO and ER methods.

Key Numerical Results

Numerical simulations demonstrate OSS’s superiority across various noise levels. For the reconstruction of simulated noisy diffraction patterns, OSS consistently produces reconstructions that are more faithful to the original models. Comparative analysis using metrics such as R-factor (RF) and reconstruction fidelity (Rreal) highlights the advantage OSS holds over other algorithms. Particularly noteworthy is OSS’s performance in reconstructing a biological vesicle model and experimental data from an S. pombe yeast spore cell, where it shows enhanced consistency.

Implications and Future Directions

The implications of OSS extend beyond CDI for biological specimens. The algorithm can be valuable in any discipline confronting phase retrieval from noisy Fourier magnitudes. OSS addresses the critical need for robust algorithms in areas increasingly reliant on accurate phase reconstruction, including nanoscience and materials science. With the continuous advancement in imaging technologies like X-FELs, OSS adequately manages experimental noise, facilitating the accurate imaging of samples under limited diffraction signals due to damage prevention protocols.

Future development in phase retrieval algorithms may see adaptations or refinements of OSS, potentially integrating machine learning-based enhancement or further improvements in noise filtering techniques. As the field grows, incorporating OSS could refine the CDI methodological toolbox, offering broader applicability and facilitating new discoveries in imaging techniques.

In summary, this paper presents OSS as a significant methodological advancement in phase retrieval efforts, providing reliable reconstructions of noisy diffraction patterns. The demonstrated efficacy of OSS promotes its application across various imaging domains, emphasizing the need for continued innovation in the treatment of noise-impaired phase retrieval processes.