Oversampling smoothness: 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 lasers and electrons. Despite recent rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities is presented. 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 stages of the iterative process ( 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 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. It is expected that OSS will find application in the rapidly growing CDI field, as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed. The (The MathWorks Inc., Natick, MA, USA) source code of the OSS algorithm is freely available from http://www.physics.ucla.edu/research/imaging.

Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick–Baez focusing

“…One or multiple oversampled diffraction patterns are recorded without the need for an imaging lens (Sayre, 1952;Miao et al, 1998). The diffraction patterns are then used by iterative algorithms to reconstruct an image of the specimen (Gerchberg & Saxton, 1972;Fienup, 1978Fienup, , 1982Sayre, 1980;Bauschke et al, 2002;Elser, 2003;Faulkner & Rodenburg, 2004;Thibault et al, 2008;Rodriguez et al, 2013). The ptychographic method which has been applied in this study has its origin in the field of electron microscopy (Hoppe, 1969a,b;Hoppe & Strube, 1969;Nellist et al, 1995;Nellist & Rodenburg, 1998) and was introduced to the field of CDI by Rodenburg et al (2007).…”

Cryogenic coherent X-ray diffraction imaging of biological samples at SACLA: a correlative approach with cryo-electron and light microscopy

“…We again repeated hundreds to thousands of independent PR calculations with the refined support and random densities by using the oversampling smoothness (OSS) algorithm (Rodriguez et al, 2013). We adopted the final projected electron-density map by averaging 100 of the most reliable reconstructions through PCA.…”

Deterministic Estimation of Stripe Type Defects and Reconstruction of Mask Pattern in L/S Type Mask Inspection

“…Unfortunately, in the presence of noise, convergence may be very slow, and in practice, solutions tend to oscillate as a function of the number of iterations because separate constraints in the realand Fourier-spaces cannot be satisfied at the same time. Several solutions have been demonstrated to make the phase retrieval algorithm more robust to noise, such as the oversampling smoothness method [5], but they still suffer from some limitations. Kim et al [6] and Kinoshita et al [7] both successfully applied iterative approaches to the case of defect detection in EUVL.…”