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An Algorithm for the Reconstruction of hv-convex Planar Bodies by Finitely Many and Noisy Measurements of their Coordinate X-rays

Vincze C., Nagy A.

Fundamenta Informaticae

2015

Vol. 141, nr 2/3

169--189

Parallel X-rays are functions that measure the intersection of a given set with lines parallel to a fixed direction in R2. The reconstruction problem concerning parallel X-rays is to reconstruct the set if the parallel X-rays into some directions are given. There are several algorithms to give an approximate solution of this problem. In general we need some additional knowledge on the object to obtain a unique solution. By assuming convexity a suitable finite number of directions is enough for all convex planar bodies to be uniquely determined by their X-rays in these directions [13]. Gardner and Kiderlen [12] presented an algorithm for reconstructing convex planar bodies from noisy X-ray measurements belonging to four directions. For a reconstruction algorithm assuming convexity we can also refer to [17]. An algorithm for the reconstruction of hv-convex planar sets by their coordinate X-rays (two directions) can be found in [18]: given the coordinate X-rays of a compact connected hv-convex planar set K the algorithm gives a sequence of polyominoes Ln all of whose accumulation points (with respect to the Hausdorff metric) have the given coordinate X-rays almost everywhere. If the set is uniquely determined by the coordinate X-rays then Ln tends to the solution of the problem. This algorithm is based on generalized conic functions measuring the average taxicab distance by integration [21]. Now we would like to give an extension of this algorithm that works in the case when only some measurements of the coordinate X-rays are given. Following the idea in [12] we extend the algorithm for noisy X-ray measurements too.

A dual modality reconstruction algorithm for optical and electrical capacitance tomography

Mosorov V., Sankowski D., Zain R.M.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

2006

T. 10, z. 3

195-202

The paper presents a novel concept combining electrical capacitance and optical tomography for monitoring and investigating of solid/gas flows. The main idea is to gain a high quality image in full-scale concentration distribution of solid/gas flow. The new image reconstruction algorithm is developed.

Artykuł przedstawia nową koncepcję połączenia elektrycznej tomografii i tomografii optycznej dla monitoringu i badań przepływów ciało stałe/gaz. Główną ideą jest otrzymanie obrazu o lepszej jakości w pełnym zakresie rozkładu koncentracji cząsteczek. Został opracowany nowy algorytm rekonstrukcji.