Analytic image reconstruction in local phase-contrast tomography

University of Chicago, Chicago, Illinois, United States
Physics in Medicine and Biology (Impact Factor: 2.76). 02/2004; 49(1):121-44. DOI: 10.1088/0031-9155/49/1/009
Source: PubMed


Phase-contrast tomography is a non-interferometric imaging technique for reconstructing the refractive index distribution of a weakly absorbing object from a set of tomographic projection measurements. In many practical situations, the spatial resolution of the reconstructed image can be increased by minimizing the field of view (FOV) of the imaging system. When the object of interest is larger than the FOV, the measured projections are truncated and one is faced with a local tomography reconstruction problem. In this work, we analytically and numerically investigate the problem of reconstructing tomographic images from truncated phase-contrast projection data. A simple backprojection algorithm for reconstructing object discontinuities from truncated phase-contrast projection data is proposed and investigated that involves no explicit filtering of the projection data. We also investigate the use of the filtered backprojection algorithm and a local tomography reconstruction algorithm developed for absorption CT. These reconstruction algorithms are implemented and numerically investigated to corroborate our theoretical assertions.

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    • "The imaging model for boundary-enhanced phase-contrast tomography is described in detail elsewhere [18]. Briefly, under a thin-object approximation, which is valid for tissue due to the high x-ray energy employed here, the measured intensity "
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    • "A significant amount of work has been done on the question of tomographic reconstruction using x-ray PBI. Key works include, but are not limited to, (i) Cloetens et al (1997), who reconstructed raw x-ray propagation-based phase-contrast data using filtered backprojection to give an edge-enhanced three-dimensional representation of the object; (ii) Cloetens et al (1999) on 'holotomography', which utilized through-focal-series phase retrieval methods originally developed in the field of electron microscopy, in the context of quantitative x-ray phase-contrast tomography; (iii) x-ray phase-contrast tomography which incorporated the transport-of-intensity equation (Teague 1983) for the phase retrieval analysis of each projection prior to three-dimensional reconstruction (Mayo et al 2003, McMahon et al 2003); (iv) Bronnikov's merging of the phase retrieval and tomography steps into a single algorithm for the case of a transparent object (Bronnikov 2002), together with the generalization of this work by Gureyev et al (2006); (v) extension of Wolf's work on diffraction tomography (Wolf 1969), in the context of x-ray phase contrast, by Anastasio and Pan (2000); (vi) Myers et al (2010) on phase retrieval tomography of few-material objects using a limited number of views, together with work on gradient-sparse objects by Sidky et al (2010); and (vii) local phase-contrast tomography (Anastasio et al 2004, Shi et al 2005, Gureyev et al 2007). For a balanced overview of the contemporary state of the art in x-ray phase-contrast tomography, we refer to the proceedings of the Conference on Developments in X-Ray Tomography VII, edited by Stock (2010). "
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    • "If we refrain from using the projection assumption, but still assume an ideal detector and optics, then the inverse problem is reduced to a limited angle region of interest reconstruction problem in diffraction tomography. Unfortunately, the mathematical theory of limited data diffraction tomography is very much work in progress[2,157]. Hence, it is not evident how to define the concept of resolution in ET that is based on sampling theory. "
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