TV regularization beats noise in low-dose CT imaging study

A new arXiv preprint by Mohamed Berrada provides a rigorous stability and robustness analysis of three reconstruction methods for low-dose computed tomography (LDCT). The work benchmarks Filtered Back Projection (FBP), Tikhonov regularization, and Total Variation (TV) minimization using a unified 2D parallel-beam simulation pipeline based on the Radon transform. Tests are conducted on both a modified Shepp-Logan phantom and a clinical thorax image, under multiple degradation scenarios including Gaussian, Poisson, and mixed noise models, at baseline (180 projections) and sparse-view (60 projections) geometries. To ensure fair comparison, regularization parameters are optimized per scenario via an exhaustive SSIM-based grid search. Quality is assessed with RMSE, PSNR, and SSIM, while a novel empirical Stability Factor S measures how much noise in measurement space amplifies into the reconstructed image.

Results confirm that FBP is highly sensitive to both noise and undersampling, producing severe artifacts. Tikhonov regularization improves structural fidelity but remains more sensitive to perturbations than TV. Total Variation strikes the best compromise: it suppresses noise effectively, preserves edges, maintains accuracy (high SSIM), and exhibits the lowest Stability Factor S, meaning measurement errors are not excessively magnified. The paper underscores the inherent stability-resolution trade-off in LDCT and shows that the proposed Stability Factor S provides valuable complementary information beyond traditional metrics like PSNR or SSIM. For practitioners, these findings offer clear guidance: when radiation dose is reduced and reconstruction stability is critical, TV-based methods should be preferred over classical FBP or Tikhonov approaches.