A relation between algebraic and transform-based reconstruction technique in computed tomography

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.