Mollifier Schemes in Limited Data Computerized Tomography

Computerized tomography algorithms for limited view tomography suffer ill-posedness problems. Generally, a masking strategy is incorporated via applying an arbitrary (3×3 or 2×2) size of square averaging mask to subdue this problem. Selection criteria for the size of this mask window have not been discussed anywhere till now. Three different spatial filtering schemes are proposed in this work that remove any dependency on the user for deciding an appropriate masking parameter. Reliability aspects of the tomography reconstruction are also discussed. Synthetic projection data is generated for 9 detectors and 18 views using fan beam geometry. The outcome of the simulation study is successfully verified for such real data situations using two specimens with known locations. Such austere scanning situations arise in a real time environment, especially for undetachable/fixed small size objects situated in inaccessible locations. These cases can only be scanned using a compact tomography setup, thus helping in the direction of their development.

References
1. Louis, A.K. and P. Maass, “A mollifier method for linear operator equations of the first kind,” Inverse Problems 6 (1990) 427-440. 2. Eryigit, M., “On degree of approximation of the Gauss-Weierstrass means for smooth Lp(Rn) functions,” Journal of Inequalities and Applications 2013, 2013:428. 3. Goswami, M., A. Saxena and P. Munsh, “Adaptive grids and spatial filtering for limited view tomography,” Proceedings of 52nd Annual Conference of BINDT, NDT 2013, Telford, U.K., 4B4 pp 98.
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