· · · Repository hosted by TU Delft Library

Purpose: The purpose of this work is to combine two areas of active research in tomographic x-ray imaging. The first one is the use of iterative reconstruction techniques. The second one is differential phase contrast imaging (DPCI). Method: We derive an SPS type maximum likelihood (ML) reconstruction algorithm with regularization for DPCI. Forward and back-projection are implemented using spherically symmetric basis functions (blobs) and differential footprints, thus completely avoiding the need for numerical differentiation throughout the reconstruction process. The method is applied to the problem of reconstruction of an object from sparsely sampled projection. Results: The results show that the proposed method can handle the sparely sampled data efficiently. In particular no streak artifacts are visible which are present images obtained by filtered back-projection (FBP). Conclusion: Iterative reconstruction algorithms have a wide spectrum of proven advantages in the area of conventional computed tomography. The present work describes for the first time, how a matched forward and back-projection can be implemented for DPCI, which is furthermore free of any heuristics. The newly developed ML reconstruction algorithm for DPCI shows that for the case of sparsely sampled projection data, an improvement in image quality is obtained that is qualitatively comparable to a corresponding situation in conventional x-ray imaging. Based on the proposed operators for forward and back-projection, a large variety of iterative reconstruction algorithms is thus made available for DPCI.

Differential phase-contrast imaging in the x-ray domain provides three physically complementary pieces of information: the attenuation,the differential phase-contrast, related to the refractive index, and the dark-field signal, related to the total amount of radiation scattered into very small angles. In medical applications, it is of the utmost importance to present to the radiologist all clinically relevant information in as compact a way as possible. Hence, the needarisis for a method to combine two or more of the above mentioned images into one image containing all information relevant for diagnosis. We present an image composition algorithm that fuses the attenuation image and the differential phase contrast image into a composite image. The composition is performed in a noise optimal way such that the composite image is characterized by minimal noise-power at each frequency component.

A quantitative theory for the contrast-to-noise ratio (CNR) in differential phase contrast imaging (DPCI) is proposed and compared to that of images derived from classical absorption contrast imaging (ACI). Most prominently, the CNR for DPCI contains the reciprocal of thespatial wavelength to be imaged, the fringe visibility, and a tunable factor dependent on the system geometry. DPCI is thus potentiallybeneficial especially for the imaging of small object structures. We demonstrate CNR calculations for mammography, finding optimal imaging energies between 15 and 22 keV for ACI, and between 20 and 40 keV for DPCI.