Abstract
Abstract. In this contribution a coherent relation between the algebraic and the transform-based reconstruction technique for computed tomography is introduced using the mathematical means of two-dimensional signal processing. There are two advantages arising from that approach. First, the algebraic reconstruction technique can now be used efficiently regarding memory usage without considerations concerning the handling of large sparse matrices. Second, the relation grants a more intuitive understanding as to the convergence characteristics of the iterative method. Besides the gain in theoretical insight these advantages offer new possibilities for application-specific fine tuning of reconstruction techniques.
Highlights
Computed tomography is a well-established method in medicine, material science and quality control
In contrast to classical imaging where the image corresponds directly to the measurements, in computed tomography the image is generated in an indirect manner
The second, algebraic reconstruction technique is attributed to Bender et al and, in principal, is an accomplishment of the Polish mathematician Stefan Kaczmarz who proposed an iterative method to approximate solutions of systems of linear equations (Kaczmarz, 1937)
Summary
Computed tomography is a well-established method in medicine, material science and quality control. The Radon transform and its inverse are analytical expressions of the projection process during the transmission measurements and the reconstruction technique, respectively. The first step to derive a relation between the inverse Radon transform and Kaczmarz’ method is to reexamine the initial m3odelRoenlawtihoinchotfhemseetthupodosf the system of linear equations is based. This leads to a reinterpretation of Kaczmarz’ method. S. Kiefhaber et al.: A relation between algebraic and transform-based reconstruction technique the spectrum of the estimated solution Gn approximates the spectrum G of the actual solution with arbitrary accuracy. For frequencies fr > 1 the iterative backprojection converges to the solution as the term in brackets vanishes in Eq (13)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
