Contrast-transfer-function phase retrieval based on compressed sensing.

We report on a new contrast-transfer-function (CTF) phase-retrieval method based on the alternating direction method of multipliers (ADMMs), which allows us to exploit any compressed sensing regularization scheme reflecting the sparsity of the investigated object. The proposed iterative algorithm retrieves accurate phase maps from highly noisy single-distance projection microscopy data and is characterized by a stable convergence, not bounded to the prior knowledge of the object support or to the initialization strategy. Experiments on simulated and real datasets show that ADMM-CTF yields reconstructions with a substantial lower amount of artifacts and enhanced signal-to-noise ratio compared to the standard analytical inversion.

[1]  M. Guizar‐Sicairos,et al.  Signal-to-noise criterion for free-propagation imaging techniques at free-electron lasers and synchrotrons. , 2016, Optics express.

[2]  T Salditt,et al.  X-ray holographic imaging of hydrated biological cells in solution. , 2015, Physical review letters.

[3]  J. Kirz,et al.  An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy. , 2005, Journal of Electron Spectroscopy and Related Phenomena.

[4]  P. Cloetens,et al.  Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region. , 2007, Optics letters.

[5]  P. Cloetens,et al.  Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays , 1999 .

[6]  Peter Bühlmann.  Regression shrinkage and selection via the Lasso: a retrospective (Robert Tibshirani): Comments on the presentation , 2011 .

[7]  P. Cloetens,et al.  Efficient sub 100 nm focusing of hard x rays , 2005 .

[8]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[9]  R. Tibshirani,et al.  Regression shrinkage and selection via the lasso: a retrospective , 2011 .

[10]  Manuel Guizar-Sicairos,et al.  Three-dimensional mass density mapping of cellular ultrastructure by ptychographic X-ray nanotomography. , 2015, Journal of structural biology.

[11]  D Mendlovic,et al.  Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain. , 1996, Optics letters.

[12]  Tim Salditt,et al.  Regularized Newton methods for x-ray phase contrast and general imaging problems. , 2015, Optics express.

[13]  P. Cloetens,et al.  Optimization of phase contrast imaging using hard x rays , 2005 .

[14]  K Joost Batenburg,et al.  Phase retrieval in in-line x-ray phase contrast imaging based on total variation minimization. , 2013, Optics express.

[15]  J. Kirz,et al.  Biological imaging by soft x-ray diffraction microscopy , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[17]  S. Wilkins,et al.  Quantitative X‐ray projection microscopy: phase‐contrast and multi‐spectral imaging , 2002, Journal of microscopy.

[18]  Paola Coan,et al.  X-ray phase-contrast imaging: from pre-clinical applications towards clinics , 2013, Physics in medicine and biology.

[19]  Oliver Cossairt,et al.  High dynamic range coherent imaging using compressed sensing. , 2015, Optics express.

[20]  Mohammed Ghanbari,et al.  Scope of validity of PSNR in image/video quality assessment , 2008 .

[21]  M. Teague.  Deterministic phase retrieval: a Green’s function solution , 1983 .

[22]  Klaus Giewekemeyer,et al.  X-ray propagation microscopy of biological cells using waveguides as a quasipoint source , 2011 .