Removing noise from reconstructed Computed Tomography (CT) images without raw projection data poses a major challenge in medical imaging, especially with sharp or medium reconstruction kernels that introduce high-frequency noise. This paper presents a novel technique combining quaternion mathematics and bilateral filtering to address this. The proposed Quaternion Bilateral Filter (QBF) preserves vital anatomical structures while reducing kernel-induced noise by representing CT scans in quaternion format, jointly encoding RGB channels. Unlike traditional methods relying on raw data or grayscale filtering, our approach operates directly on sharp-kernel reconstructed images, transforming them to match the quality of soft-kernel outputs (e.g., B30f) using paired patient data. QBF’s performance is validated through full-reference metrics (SSIM, PSNR, MAE, RMSE) and no-reference perceptual measures (NIQE, BRISQUE, PIQE). Results demonstrate QBF’s superiority over conventional Bilateral Filter (BF), Non-Local Means (NLM), wavelet, and CNN-based methods, with SSIM of 0.96 and PSNR of 36.3 on B50f reconstructions. Segmentation-based visual assessment confirms that QBF-preserved images retain essential structural details for downstream diagnostics. The study highlights quaternion filtering as a lightweight, interpretable, and efficient alternative to deep learning for post-reconstruction CT enhancement.
Autors: Mahmoud Nasr, Adam Piórkowski, Krzysztof Brzostowski, Fathi E. Abd El-Samie
Keywords: Quaternion, Bilateral filter, Reconstruction kernels, Denoising, SSIM, PSNR, Image quality metrics