Basic acceleration technique with theoretical analysis on iterative algorithms for image reconstruction

In image reconstruction and processing, incorporating prior information, particularly the nonnegativity of pixel values, is essential. Existing computed tomography (CT) iterative reconstruction algorithms, including the algebraic reconstruction technique (ART), simultaneous ART (SART), and the simultaneous iterative reconstruction technique (SIRT), typically address negative components during the iteration process by either setting them to zero, introducing regularization terms to prevent negativity, or leaving them unchanged. This paper establishes a general framework in which enforcing the nonnegativity prior accelerates the convergence of the reconstructed image toward the true solution. Within this framework, we propose two efficient and simple acceleration techniques: setting negative pixel values to their absolute values and updating them to the estimated values from the previous update. Experiments were conducted using ART, SIRT, and SART algorithms, integrated with the corresponding acceleration techniques, on full-angle, limited-angle, and noisy simulated data, as well as real data. The results validate the effectiveness of the proposed acceleration methods by evaluating image quality using the PSNR and SSIM metrics. Notably, the proposed technique that sets negative pixel values to their absolute values is strongly recommended, as it significantly outperforms the existing technique that sets them to zero, both in terms of image quality and iteration time.