Comparison of approaches based on optimization and algebraic iteration for binary tomography

Abstract

Binary tomography represents a special category of tomographic problems, in which only two values are possible for the sought image pixels. The binary nature of the problems can potentially lead to a significant reduction in the number of view angles required for a satisfactory reconstruction, thusly enabling many interesting applications. However, the limited view angles result in a severely underdetermined system of equations, which is challenging to solve. Various approaches have been proposed to address such a challenge, and two categories of approaches include those based on optimization and those based on algebraic iteration. However, the relative strengths, limitations, and applicable ranges of these approaches have not been clearly defined in the past. Therefore, it is the main objective of this work to conduct a systematic comparison of approaches from each category. This comparison suggested that the approaches based on algebraic iteration offered both superior reconstruction fidelity and computation efficiency at low (two or three) view angles, and these advantages diminished at high view angles. Meanwhile, this work also investigated the application of regularization techniques, the selection of optimal regularization parameter, and the use of a local search technique for binary problems. We expect the results and conclusions reported in this work to provide valuable guidance for the design and development of algorithms for binary tomography problems.