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SR technological application and X-ray apparatus

Apparatus-software tomography complex: the use of the regularization procedure in algebraic approach to image reconstruction


  • Dr. Marina CHUKALINA

Primary authors



The use of algebraic approaches with regularization terms in tomography can improve the quality of images with a low signal-to-noise ratio. Also they work well if the object under investigation contains highly absorbing inclusions or the measurement conditions are unstable during the measurement time. They win in competition of reconstruction techniques with a limited number of projections. Then why the main approaches of reconstruction in industrial and medical tomography set-ups are not algebraic ones with regularization? The talk provides an informative look at the problem. We formulate a list of tasks that need to be solved before the approach becomes widely used: high speed operation (working with data, optimality of mathematical methods and algorithms, and optimality of numerical realizations), choice of the method to solve the optimization problem depending on the optical properties of the object under probing and the choice of a regularization procedure depending on the morphological properties of the object under study. To solve the last problem in our efforts we use some list of the features of the tomographic images. The paper presents an overview of mathematical tools used by different groups in the world to regularize the solution in the tomography problem. Results of the reconstruction for both model examples and real measurements are used to illustrate the main ideas. The measurements were carried out on the apparatus-software tomographic complex TOMAS developed and continuous operating at the Institute of Crystallography FSRC “Crystallography and Photonics” RAS. Also, approaches to solving the optimization problem (in the presence of highly absorbing inclusions) are analyzed. The results obtained by the quadratic programming method and the results obtained using the penalty method are compared. The average value and the variance value calculated for ROI, together with the width of the boundary profile form a list of the compared parameters.

This work was supported by the Federal Agency of Scientific Organizations (Agreement No 007-ГЗ/Ч3363/26) in data collection. This work was supported by Russian Foundation for Basic Research (project #17-29-03492) in the algorithmic part. The authors wish to express their appreciation to N. Vlasova for technical support.