In computed tomography there are different situations where reconstruction has to be performed with limited raw data. In the past few years it has been shown that algorithms which are based on compressed sensing theory are able to handle incomplete datasets quite well. As a cost function these algorithms use the ℓ(1)-norm of the image after it has been transformed by a sparsifying transformation. This yields to an inequality-constrained convex optimization problem. Due to the large size of the optimization problem some heuristic optimization algorithms have been proposed in the past few years. The most popular way is optimizing the raw data and sparsity cost functions separately in an alternating manner. In this paper we will follow this strategy and present a new method to adapt these optimization steps. Compared to existing methods which perform similarly, the proposed method needs no a priori knowledge about the raw data consistency. It is ensured that the algorithm converges to the lowest possible value of the raw data cost function, while holding the sparsity constraint at a low value. This is achieved by transferring the step-size determination of both optimization procedures into the raw data domain, where they are adapted to each other. To evaluate the algorithm, we process measured clinical datasets. To cover a wide field of possible applications, we focus on the problems of angular undersampling, data lost due to metal implants, limited view angle tomography and interior tomography. In all cases the presented method reaches convergence within less than 25 iteration steps, while using a constant set of algorithm control parameters. The image artifacts caused by incomplete raw data are mostly removed without introducing new effects like staircasing. All scenarios are compared to an existing implementation of the ASD-POCS algorithm, which realizes the step-size adaption in a different way. Additional prior information as proposed by the PICCS algorithm can be incorporated easily into the optimization process.

Small-angle neutron scattering (SANS) is one of the most important techniques for microstructure determination, being utilized in a wide range of scientific disciplines, such as materials science, physics, chemistry, and biology. The reason for its great significance is that conventional SANS is probably the only method capable of probing structural inhomogeneities in the bulk of materials on a mesoscopic real-space length scale, from roughly 1 − 300 nm. Moreover, the exploitation of the spin degree of freedom of the neutron provides SANS with a unique sensitivity to study magnetism and magnetic materials at the nanoscale. As such, magnetic SANS ideally complements more real-space and surface-sensitive magnetic imaging techniques, e.g., Lorentz transmission electron microscopy, electron holography, magnetic force microscopy, Kerr microscopy, or spinpolarized scanning tunneling microscopy. In this review article we summarize the recent applications of the SANS method to study magnetism and magnetic materials. This includes a wide range of materials classes, from nanomagnetic systems such as soft magnetic Fe-based nanocomposites, hard magnetic Nd−Fe−B-based permanent magnets, magnetic steels, ferrofluids, nanoparticles, and magnetic oxides, to more fundamental open issues in contemporary condensed matter physics such as skyrmion crystals, noncollinar magnetic structures in noncentrosymmetric compounds, magnetic/electronic phase separation, and vortex lattices in type-II superconductors. Special attention is paid not only to the vast variety of magnetic materials and problems where SANS has provided direct insight, but also to the enormous progress made regarding the micromagnetic simulation of magnetic neutron scattering.

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The reconstruction algorithms including at least one iterative step can reduce the 4 CBCT specific artifacts. Nevertheless, the algorithms that use the full data set, at least for initialization, such as MKB and PICCS in the authors' implementation, are only a trade-off and may not fully achieve the optimal temporal resolution. A predictable image quality as seen in conventional reconstruction methods, i.e., without total variation minimization, is a desirable property for reconstruction algorithms. Fast, iterative approaches such as the MKB can therefore be seen as a suitable tradeoff.

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