A Newton-Raphson Accelerated Iterative Reconstruction Method

摘要

The greatest advantage of iterative techniques in the computed tomography is the ability to produce better images than other analytical methods in cases, where fewer and not uniformly distributed projection data are available. Following the general iterative approach of the Algebraic Reconstruction Technique (ART) enhanced with convergence acceleration schemes derived from the Newton-Raphson methodology, a new type of a reconstruction algorithm for tomographic images is proposed. The Cost Function connected to the minimization procedure of this algorithm operates on the squared differences between the measured and reconstructed sinograms, taking into account matrix derivatives and their correlations with respect to neighborhood rays and projection angles. In addition to the formalism, the quality of the proposed reconstruction technique tested with sparse and noisy data will be presented and its convergence speed will be discussed with respect to other, well established methods.