Comparison of regularized phase retrieval algorithms for x-ray phase contrast tomography - application on experimental data

During the past twenty years, there has been a growing interest in phase contrast imaging. This modality offers a better sensitivity (three orders of magnitude higher) than conventional radiology, which only records attenuation induced by the object. In-line phase contrast imaging consists in letting a spatially coherent beam propagate, after passing through a sample [1]. Projections are acquired at several angles, for several sample-to-detector distances. These projections contain both phase and attenuation information. Phase can be extracted from projections, using a so-called phase retrieval algorithm. This can be combined with tomography: at each angular position, projections recorded at a single distance or at several distances (holotomography) can be used to reconstruct the 2D phase projection. Finally, a tomographic reconstruction algorithm can be applied to these phase projections to obtain a 3D-map of the refractive index in the object. The phase retrieval process is nevertheless sensitive to low-frequency noise. This can result in slowly varying patterns in the background of the images. To alleviate this problem, an initial guess of the retrieved phase can be introduced as a prior. Several phase retrieval algorithms assume that the object to reconstruct is homogeneous, that is composed of materials with the same δ/β-ratio [2], [3]. Thus, the retrieved phase is assumed to be proportional to the attenuation. Another algorithm has been developed for heterogeneous objects (composed of known materials) in holotomography. The prior is designed by either segmenting the attenuation volume [4], or assuming that the δ/β-ratio is related to the attenuation coefficient by a functional relationship [5]. In this work, we compare holotomography with either introduction of a homogeneous or heterogeneous prior. These algorithms were first tested on experimental data of a phantom, acquired on the ID19 beamline at the ESRF. This phantom is composed of three wires (Al, Mg and PET respectively), mounted in a glass capillary. We show that the introduction of a prior significantly reduces low-frequency noise. Moreover, the introduction of a heterogeneous object prior yields a better quantification of the refractive index than one obtained using a homogeneous object prior. We also applied the homogeneous prior in the imaging of porous bone scaffolds (Skelite) cultivated with bone cells. Skelite scaffolds are used in bone surgery for bone regeneration, since they induce the formation of mature lamellar bone within 20 weeks, as well as substrates for 3D cell culture [6]. This algorithm enabled to quantify the volume and density of the calcified fraction, as well as the volume of extracellular matrix generated by the bone cells, by thresholding the refractive index maps. The analysis of the soft tissue compartment was not possible using attenuation-based imaging. The heterogeneous object prior will be applied on these scaffold images. By using this algorithm, we expect the 3D refractive index to be quantitative both in hard and soft tissue. [1] A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation, Rev. Sci. Instrum., vol. 66, no. 12, p. 5486, Dec. 1995. [2] D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object, J. Microsc., vol. 206, no. 1, pp. 33-40, Apr. 2002. [3] M. Langer, P. Cloetens, and F. Peyrin, Regularization of phase retrieval with phase-attenuation duality prior for 3-D holotomography., IEEE Trans. Image Process., vol. 19, no. 9, pp. 2428-36, Sep. 2010. [4] M. Langer, P. Cloetens, A. Pacureanu, and F. Peyrin, X-ray in-line phase tomography of multimaterial objects., Opt. Lett., vol. 37, no. 11, pp. 2151-3, Jun. 2012. [5] M. Langer, P. Cloetens, B. Hesse, H. Suhonen, A. Pacureanu, K. Raum, and F. Peyrin, Priors for in-line phase tomography of heterogeneous objects, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 372, no. 2010, pp. 20130129-20130129, Jan. 2014. [6] M. Langer, Y. Liu, F. Tortelli, P. Cloetens, R. Cancedda, and F. Peyrin, Regularized phase tomography enables study of mineralized and unmineralized tissue in porous bone scaffold. J. Microsc., Vol 238, n°3, pp 230-9, Jun 2010.