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We have explored and compared two implementation strategies for PWLS sinogram restoration:(1)A direct matrix-inversion strategy based on the closed-form so-lution to the PWLS optimization problem and(2) an iterative approach based on the conjugate-gradient algorithmObtaining optimal performance from each strategy required modifyingthe naive off-the-shelf implementations of the algorithms to exploitthe particular symmetry and sparseness of the sinogram-restorationproblem. For the closedform approach, we subdivided the large matrixinversion into smaller coup led problems and exploited sparse-nessto minimize matrix operations. For the conjugate gradient approach,we exploited sparseness and preconditioned the problem to speed con-vergence. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approa-ches,with a computational burden an order of magnitude or more higher.The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of our previous penalized-likelihood implementation.

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.

Statistical, iterative reconstruction techniques have become a major research topic in the CT sector. These techniques promise a better system model, which is used for the inversion of the tomographic problem, and therefore better reconstruction results. Due to the ill–posedness of these problems, regularization is required in the cost functions in order to stabilize the algorithm and to reduce the noise in the resulting images. The strength of the regularization is usually changed by using an appropriate multiplicative factor, which in most cases has to be determined empirically with major efforts. This paper describes a new automated selection of this factor by using a quality criterion and a regulator, which controls the multiplicative factor over the iterations to a desired level. The method is light–weight, robust and also applicable for other iterative methods like de–noising.

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.

Aiming at modeling the system’s geometry correctly accounting for the major effects influencing image quality within an iterative reconstruction framework we want to achieve this within reasonable processing times. This principle objective led us to using blobs for imagerepresentation and a dedicated GPU hardware implementation. Making extensive use of the texture interpolation capabilities of CUDA and implementing an asymmetric projector/backprojector pair we achieve reasonable processing times and good system modeling at the same time.We conclude from the above results that using GPUs and adequate implementations of the projectors, iterative reconstruction using blobsfor image representation becomes feasible. This, along with avoiding re-sampling, will allow us to apply detailed system modeling for enhanced resolution/noise tradeoff.

A number of different methods for post reconstruction bone beam hardening (BBH) correction are available for conventional FBP reconstruction and are used in commercially available products. An incorporation of these existing methods into statistical iterative reconstruction for CT is desired for several reasons. There are two ways imaginable to incorporate the BBH correction into iterative reconstruction:The first option is to use the beam hardening corrected projectionsas input for the statistical iterative reconstruction. For this ithas to be considered that the noise level in the projection data changes due to the correction. The second option is to incorporate theinverse of the beam hardening correction into the forward projectionof the cost function, and derive an update equation from this modified cost function. Both methods are implemented and compared based on simulated data with respect to artifact suppression, image noise,and speed of convergence.

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.