2024/08/12 by Matthias Beckmann, Beckmann, Matthias, Judith Nickel +1
Computer Science · Earth and Planetary Sciences · Medicine · #FOS: Mathematics #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA) #Optical measurement and interference techniques #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.2408.06471
openalex publication_date 2024/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The method of filtered back projection (FBP) is a widely used reconstruction technique in X-ray computerized tomography (CT), which is particularly important in clinical diagnostics. To reduce scanning times and radiation doses in medical CT settings, enhancing the reconstruction quality of the FBP method is essential. To this end, this paper focuses on analytically optimizing the applied filter function. We derive a formula for the filter that minimizes the expected squared L2-norm of the difference between the FBP reconstruction, given infinite noisy measurement data, and the true target function. Additionally, we adapt our derived filter to the case of finitely many measurements. The resulting filter functions have a closed-form representation, do not require a training dataset, and, thus, provide an easy-to-implement, out-of-the-box solution. Our theoretical findings are supported by numerical experiments based on both simulated and real CT data.