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Mom K, Langer M, Sixou B. Nonlinear primal-dual algorithm for the phase and absorption retrieval from a single phase contrast image. OPTICS LETTERS 2022; 47:5389-5392. [PMID: 36240370 DOI: 10.1364/ol.469174] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2022] [Accepted: 09/15/2022] [Indexed: 06/16/2023]
Abstract
We propose a nonlinear primal-dual algorithm for the retrieval of phase shift and absorption from a single x ray in-line phase contrast, or Fresnel diffraction, image. The algorithm permits us to regularize phase and absorption separately. We demonstrate that taking into account the nonlinearity in the reconstruction improves reconstruction compared with linear methods. We also demonstrate that choosing different regularizers for absorption and phase can improve the reconstructions. The use of the total variation and its generalization in a primal-dual approach allows us to exploit the sparsity of the investigated sample. On both simulated and real datasets, the proposed nonlinear primal-dual hybrid gradient (NL-PDHG) method yields reconstructions with considerably fewer artifacts and improved the normalized mean squared error compared with its linearized version.
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Huhn S, Lohse LM, Lucht J, Salditt T. Fast algorithms for nonlinear and constrained phase retrieval in near-field X-ray holography based on Tikhonov regularization. OPTICS EXPRESS 2022; 30:32871-32886. [PMID: 36242340 DOI: 10.1364/oe.462368] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 08/02/2022] [Indexed: 06/16/2023]
Abstract
Based on phase retrieval, lensless coherent imaging and in particular holography offers quantitative phase and amplitude images. This is of particular importance for spectral ranges where suitable lenses are challenging, such as for hard x-rays. Here, we propose a phase retrieval approach for inline x-ray holography based on Tikhonov regularization applied to the full nonlinear forward model of image formation. The approach can be seen as a nonlinear generalization of the well-established contrast transfer function (CTF) reconstruction method. While similar methods have been proposed before, the current work achieves nonlinear, constrained phase retrieval at competitive computation times. We thus enable high-throughput imaging of optically strong objects beyond the scope of CTF. Using different examples of inline holograms obtained from illumination by a x-ray waveguide-source, we demonstrate superior image quality even for samples which do not obey the assumption of a weakly varying phase. Since the presented approach does not rely on linearization, we expect it to be well suited also for other probes such as visible light or electrons, which often exhibit strong phase interaction.
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Yatabe K, Takayama Y. Phase retrieval based on a total-variation-regularized Poisson model for X-ray ptychographic imaging of low-contrast objects. J Appl Crystallogr 2022. [DOI: 10.1107/s1600576722005234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
Hard X-ray ptychography has become an indispensable tool for observing the microscopic structure of a thick specimen. It measures diffraction patterns by scanning an X-ray beam and visualizes the complex-valued refractive index of the specimen by a computational reconstruction called phase retrieval. The quality of imaging is dependent on the used phase-retrieval algorithm, especially when the intensity of the diffraction patterns in the high-spatial-frequency range is low and/or when the spatial overlap of the illumination area is small. In this paper, a phase-retrieval algorithm, AMPAM, based on the Poisson model and total variation (TV) is proposed. It applies alternating minimization using primal-dual splitting and gradient-descent algorithms to compute the result without matrix inversion. The imaging capability of the proposed algorithm from low-dose and/or sparsely scanned data was investigated by numerical simulations. The proposed algorithm was compared with ADPr, which is the state-of-the-art algorithm based on the TV-regularized Poisson model. The results indicated that AMPAM can provide good-quality images with a computational cost 7–11 times less than ADPr. In addition, ink toner and macroporous silica particles were imaged at SPring-8 BL24XU to confirm the applicability of the algorithm to actual measurements.
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Kumar S. Phase retrieval with physics informed zero-shot network. OPTICS LETTERS 2021; 46:5942-5945. [PMID: 34851929 DOI: 10.1364/ol.433625] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 11/10/2021] [Indexed: 06/13/2023]
Abstract
Phase can be reliably estimated from a single diffracted intensity image if faithful prior information about the object is available. Examples include amplitude bounds, object support, sparsity in the spatial or transform domain, deep image prior, and the prior learned from labeled datasets by a deep neural network. Deep learning facilitates state-of-the-art reconstruction quality but requires a large labeled dataset (ground truth measurement pair acquired in the same experimental conditions) for training. To alleviate this data requirement problem, this Letter proposes a zero-shot learning method. The Letter demonstrates that the object prior learned by a deep neural network while being trained for a denoising task can also be utilized for phase retrieval if the diffraction physics is effectively enforced on the network output. The Letter additionally demonstrates that the incorporation of total variation in the proposed zero-shot framework facilitates reconstruction of similar quality in less time (e.g., ∼9 fold, for a test reported in this Letter).
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Langer M, Zhang Y, Figueirinhas D, Forien JB, Mom K, Mouton C, Mokso R, Villanueva-Perez P. PyPhase - a Python package for X-ray phase imaging. JOURNAL OF SYNCHROTRON RADIATION 2021; 28:1261-1266. [PMID: 34212892 PMCID: PMC8284402 DOI: 10.1107/s1600577521004951] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2021] [Accepted: 05/11/2021] [Indexed: 06/01/2023]
Abstract
X-ray propagation-based imaging techniques are well established at synchrotron radiation and laboratory sources. However, most reconstruction algorithms for such image modalities, also known as phase-retrieval algorithms, have been developed specifically for one instrument by and for experts, making the development and diffusion of such techniques difficult. Here, PyPhase, a free and open-source package for propagation-based near-field phase reconstructions, which is distributed under the CeCILL license, is presented. PyPhase implements some of the most popular phase-retrieval algorithms in a highly modular framework supporting its deployment on large-scale computing facilities. This makes the integration, the development of new phase-retrieval algorithms, and the deployment on different computing infrastructures straightforward. Its capabilities and simplicity are presented by application to data acquired at the synchrotron source MAX IV (Lund, Sweden).
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Affiliation(s)
- Max Langer
- Univ Lyon, INSA Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621 Villeurbanne, France
| | - Yuhe Zhang
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, SE-221 00 Lund, Sweden
| | - Diogo Figueirinhas
- Division of Packaging Logistics, Faculty of Engineering, Lund University, SE-22100 Lund, Sweden
- MAX IV Laboratory, Lund University, SE-22100 Lund, Sweden
| | | | - Kannara Mom
- Univ Lyon, INSA Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621 Villeurbanne, France
| | - Claire Mouton
- Univ Lyon, INSA Lyon, Université Claude Bernard Lyon 1, UJM-Saint Etienne, CNRS, Inserm, CREATIS UMR 5220, U1206, F-69621 Villeurbanne, France
| | - Rajmund Mokso
- Division of Solid Mechanics, Faculty of Engineering, Lund University, SE-22100 Lund, Sweden
| | - Pablo Villanueva-Perez
- Division of Synchrotron Radiation Research and NanoLund, Department of Physics, Lund University, SE-221 00 Lund, Sweden
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Reichardt M, Frohn J, Khan A, Alves F, Salditt T. Multi-scale X-ray phase-contrast tomography of murine heart tissue. BIOMEDICAL OPTICS EXPRESS 2020; 11:2633-2651. [PMID: 32499949 PMCID: PMC7249829 DOI: 10.1364/boe.386576] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Revised: 03/12/2020] [Accepted: 03/18/2020] [Indexed: 05/07/2023]
Abstract
The spatial organization of cardiac muscle tissue exhibits a complex structure on multiple length scales, from the sarcomeric unit to the whole organ. Here we demonstrate a multi-scale three-dimensional imaging (3d) approach with three levels of magnification, based on synchrotron X-ray phase contrast tomography. Whole mouse hearts are scanned in an undulator beam, which is first focused and then broadened by divergence. Regions-of-interest of the hearts are scanned in parallel beam as well as a biopsy by magnified cone beam geometry using a X-ray waveguide optic. Data is analyzed in terms of orientation, anisotropy and the sarcomeric periodicity via a local Fourier transformation.
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Affiliation(s)
- Marius Reichardt
- Gerorg-August-University, Institute for x-ray Physics, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Jasper Frohn
- Gerorg-August-University, Institute for x-ray Physics, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Amara Khan
- Max Planck Institute for Experimental Medicine, Group of Translational Molecular Imaging, German Hermann-Rein-Straße 3, 37075 Göttingen, Germany
| | - Frauke Alves
- Max Planck Institute for Experimental Medicine, Group of Translational Molecular Imaging, German Hermann-Rein-Straße 3, 37075 Göttingen, Germany
- University Medical Center Göttingen, Clinic of Hematology and Medical Oncology, Robert-Koch-Straße 40, 37075 Göttingen, Germany
- University Medical Center Göttingen, Institute for Diagnostic and Interventional Radiology, Robert-Koch-Straße 40, 37075 Göttingen, Germany
| | - Tim Salditt
- Gerorg-August-University, Institute for x-ray Physics, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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Bai C, Zhou M, Min J, Dang S, Yu X, Zhang P, Peng T, Yao B. Robust contrast-transfer-function phase retrieval via flexible deep learning networks. OPTICS LETTERS 2019; 44:5141-5144. [PMID: 31674951 DOI: 10.1364/ol.44.005141] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2019] [Accepted: 09/22/2019] [Indexed: 06/10/2023]
Abstract
By exploiting the total variation (TV) regularization scheme and the contrast transfer function (CTF), a phase map can be retrieved from single-distance coherent diffraction images via the sparsity of the investigated object. However, the CTF-TV phase retrieval algorithm often struggles in the presence of strong noise, since it is based on the traditional compressive sensing optimization problem. Here, convolutional neural networks, a powerful tool from machine learning, are used to regularize the CTF-based phase retrieval problems and improve the recovery performance. This proposed method, the CTF-Deep phase retrieval algorithm, was tested both via simulations and experiments. The results show that it is robust to noise and fast enough for high-resolution applications, such as in optical, x-ray, or terahertz imaging.
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