Boundary value problem for phase retrieval from unidirectional X-ray differential phase images

Abstract

Abstract:The phase retrieval problem can be reduced to the second order partial differential equation. In order to retrieve the absolute values of the X-ray phase and to minimize the reconstruction artifacts we defined the mixed inhomogeneous boundary condition using available a priori information about the sample. Finite element technique was used to solve the boundary value problem. The approach is validated on numerical and experimental phantoms. In order to demonstrate a possible application of the method, we have processed an entire tomographic set of differential phase images and estimated the magnitude of the refractive index decrement for some tissues inside complex biomedical samples. References and links1. R. Fitzgerald, "Phase-sensitive X-ray imaging," Phys. Today 53, 23-27 (2000). 2. A. Bravin, P. Coan, and P. Suortti, "X-ray phase-contrast imaging: from pre-clinical applications towards clinics," Phys. Med. Biol 58, R1-R35 (2013). 3. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335-337 (1996). 4. V. N. Ingal and E. A. Beliaevskaya, "X-ray plane-wave topography observation of the phase contrast from a non-crystalline object," J. Phys. D 28, 2314-2318 (1995). 5. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, "Quantitative X-ray phase imaging with a grating interferometer," Opt. Lett. 108, 158102 (2012). 11. J. Sperl, D. Bequ, G. Kudielka, K. Mahdi, P. Edic, and C. Cozzini, "A Fourier-domain algorithm for total-variation regularized phase retrieval in differential X-ray phase contrast imaging," Opt. Express 22, 450-462 (2014 F. Pfeiffer, and J. Herzen, "Quantitative imaging using high-energy X-ray phase-contrast CT with a 70 kVp polychromatic X-ray spectrum," Opt. Express 23, 523-535 (2015).

Low-dose quantitative phase contrast medical CT

“…A quantitative comparison of the two methods presented together with the GFBP is reported in Gasilov et al (2015). The results show how these two methods are very similar from a qualitative and quantitative point of view, but completely outperform the results obtained using the GFBP.…”

“…Equation ( 4) can be converted into a boundary value problem (Gasilov et al 2015) taking the first partial derivative of both sides along the y-coordinate and by adding a weighted regularization term γ on the left-hand side to suppress the streak artefacts along the horizontal direction x. The result is expressed by equation ( 5):…”

“…not specifically related to a particular type of sample. In fact, the possibility of performing quantitative 3D measurements of the index of refraction of complex objects can be exploited in a multitude of fields (Mizuno et al 2007, Takeya et al 2012, Gasilov et al 2017a, 2017b and advanced computed tomography reconstruction algorithms requiring a reduced amount of angular projections can be of interest whenever experimental limitations do not allow the Nyquist sampling criteria to be satisfied during tomographic acquisition.…”