MATHEMATICAL MODELS AND ITERATIVE ALGORITHMS FOR IMAGE RECONSTRUCTION UNDER LIMITED DATA CONDITIONS IN X-RAY COMPUTED TOMOGRAPHY
Received: 2026-05-16
Published: 2026-06-06
Abstract
The problem of image reconstruction in X-ray computed tomography (CT) is frequently encountered under limited data conditions, such as sparse-view projections, short scan times, low-dose radiation, or truncated fields of view. In such scenarios, the classical Filtered Back-Projection (FBP) method fails to provide stable results due to severe artifacts and noise amplification. This paper analyzes mathematical models and iterative algorithms for reconstruction under data-starved conditions and discusses their practical efficacy. Primary focus is placed on the algebraic reconstruction family, specifically ART (Algebraic Reconstruction Technique), SIRT (Simultaneous Iterative Reconstruction Technique), and SART (Simultaneous Algebraic Reconstruction Technique). Furthermore, Tikhonov regularization and its parameter selection principles are examined to stabilize the ill-posed inverse problem. Based on simulation and experimental data, the impacts of iteration count, noise level, and missing projections on reconstruction accuracy are evaluated using standard metrics (RMSE, PSNR, SSIM). The results demonstrate that while iterative approaches significantly mitigate artifacts in limited data configurations, improper selection of regularization parameters and stopping criteria can lead to either over-smoothing or noise amplification.
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List of references
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