Advances in discrete tomography and its applications by Gabor T. Herman

By Gabor T. Herman

Advances in Discrete Tomography and Its purposes is a unified presentation of latest equipment, algorithms, and choose functions which are the rules of multidimensional snapshot reconstruction by means of discrete tomographic equipment. The self-contained chapters, written by means of best mathematicians, engineers, and computing device scientists, current state of the art examine and ends up in the field.Three major components are coated: foundations, algorithms, and functional purposes. Following an advent that experiences the hot literature of the sector, the ebook explores numerous mathematical and computational difficulties of discrete tomography together with new applications.Topics and Features:* advent to discrete aspect X-rays* strong point and additivity in discrete tomography* community stream algorithms for discrete tomography* convex programming and variational tools* purposes to electron microscopy, fabrics technological know-how, nondestructive checking out, and diagnostic medicineProfessionals, researchers, practitioners, and scholars in arithmetic, laptop imaging, biomedical imaging, computing device technology, and picture processing will locate the ebook to be an invaluable consultant and connection with cutting-edge examine, tools, and functions.

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Prior learning and convex-concave regularization of binary tomography. Electr. Notes Discr. , 20, 313–327 (2005). 184. : A linear programming approach to limited angle 3D reconstruction from DSA projections. Methods of Information in Medicine, 43, 320–326 (2003). 16 A. T. Herman ¨ Discrete tomography: A modern inverse problem 185. : reconsidered by optimization. J. Comp. , 9, 115–121 (2004). 186. : The reconstruction of polyominoes from their orthogonal projections. Inform. Process. , 77, 225–229 (2001).

Comp. , 9, 115–121 (2004). 186. : The reconstruction of polyominoes from their orthogonal projections. Inform. Process. , 77, 225–229 (2001). 187. : A convergent composite mapping Fourier domain iterative algorithm for 3-D discrete tomography. Lin. , 339, 91–109 (2001). , Ozbudak, ¨ 188. : On the applied mathematics of discrete tomography. J. Comp. , 9, 14–32 (2004). 189. : Linear diophantine equations for discrete tomography. J. X-Ray Sci. , 10, 59–66 (2001). 190. : Detection of subsurface bubbles with discrete electromagnetic geotomography.

C) Suppose now that E is hv-convex and 8-connected. Let M be such that each Zihv (M ) contains a point Ni of E. For each i there is an 8-path joining Ni and Ni+1 included in E, and so there is a point Ai in Zihv (M ) ˜ i ) = h(M ˜ that satisfies h(A ) or v˜(Ai ) = v˜(M ). Then it is easy to see that M lies in a horizontal or vertical segment [Ai Aj ], and so M is in E by hv-convexity. (a) (b) (c) Fig. 2. t. {h, v}. t. {h, v}. t. {h, v, d}. 36 S. Brunetti and A. 4 Uniqueness Result The aim of this section is to explain and sketch the proof of the following result extending Theorem 1 to Q-convex lattice sets.

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