An Accelerated Algebraic Reconstruction Technique based on the Newton-Raphson Scheme

The idea presented here is based on the Newton-Raphson root-finding methodology for localizing the minimum of a function. The proposed algorithm follows the iterative approach of the traditional Algebraic Reconstruction Technique (ART) with the introduction of a new correction method, similar to the Newton-Raphson scheme generalized to several dimensions. The definition of the derivative in this method causes an acceleration in the convergence speed, which results to a respectable drop of the number of iterations needed to minimize the quadratic deviation. The major issue was the definition of a Cost Function and its first and second derivative, the equivalent root of which would lead to the detection of the local minimum. This Cost Function contains the squared difference of the measured and the reconstructed projections in the appropriate matrix notation and takes into account the derivatives with respect to neighborhood rays and projection angles. Apart from the formalism, the quality of the proposed reconstruction and its convergence speed with respect to the traditional ART is discussed in this work.