New image-restoration method using a simultaneous algebraic reconstruction technique: comparison with the Richardson-Lucy algorithm.

We developed a new image-restoration method that incorporates the point spread function (PSF) into the simultaneous algebraic reconstruction technique (SART-PSF). Additionally, through simulation studies, we investigated the usefulness of the method in comparison with the Richardson-Lucy (RL) algorithm. In the simulation studies, degraded images were generated by convolving magnetic resonance imaging-based brain images with PSF and adding Gaussian or Poisson noise to them to simulate various noise levels. The effects of the number of iterations N, noise, and PSF error on the processed images were quantitatively evaluated using the percent root mean square error (PRMSE) and mean structural similarity index (mSSIM). After applying the SART-PSF to images degraded using Gaussian noise, the PRMSE value and increase thereof, when N was increased, were smaller than those when using the RL algorithm. The mSSIM value was higher and its decrease upon increasing N was smaller than that of the RL algorithm. When Poisson noise was assumed, the differences in PRMSE and mSSIM between both methods were smaller than those when Gaussian noise was assumed. When the PSF error was negative, its effect on PRMSE and mSSIM was similar for both methods. However, when it was positive, the deterioration of these parameters for the SART-PSF was less than that for the RL algorithm in both the Gaussian and Poisson noise cases. The results suggest that the SART-PSF is more robust against noise and a PSF error than the RL algorithm and, thus, can be used as an alternative to the RL algorithm.