Abstract
Differential X-ray phase-contrast tomography (DPCT) refers to a class of promising methods for reconstructing the X-ray refractive index distribution of materials that present weak X-ray absorption contrast. The tomographic projection data in DPCT, from which an estimate of the refractive index distribution is reconstructed, correspond to one-dimensional (1D) derivatives of the two-dimensional (2D) Radon transform of the refractive index distribution. There is an important need for the development of iterative image reconstruction methods for DPCT that can yield useful images from few-view projection data, thereby mitigating the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods. In this work, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction in DPCT. We also investigate the use of one of the models with a modern image reconstruction algorithm for performing few-view image reconstruction of a tissue specimen.
Highlights
Differential phase-contrast tomography (DPCT) employing hard X-rays [1,2,3,4,5] refers to a class of imaging methods for reconstructing the X-ray refractive index distribution of objects from knowledge of differential projection data
When DPCT is implemented with optical wavefields, which has been referred to as beam-deflection tomography [11], techniques such as moire deflectometry [12] have been employed for measuring the beam-deflection data
We analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction in DPCT
Summary
Differential phase-contrast tomography (DPCT) employing hard X-rays [1,2,3,4,5] refers to a class of imaging methods for reconstructing the X-ray refractive index distribution of objects from knowledge of differential projection data. In order to avoid image artifacts when employing this algorithm and other analytic reconstruction algorithms, tomographic measurements must be typically acquired at a large number of view angles This is highly undesirable because it can result in long data-acquisition times, especially in bench top applications where the X-ray tube power is limited, and may damage the sample due to the large radiation exposure. One model employs conventional pixel expansion functions while the other employs Kaiser-Bessel window functions The latter choice is shown to have the attractive feature that the 1D derivative operator in the DPCT imaging model can be computed analytically, thereby cirvumventing the need to numerically approximate it. The effectiveness of the reconstruction method is demonstrated by use of experimental DPCT projection data corresponding to a biological tissue specimen
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