A novel approach for CT image smoothing: Quaternion Bilateral Filtering for kernel conversion

Denoising reconstructed Computed Tomography (CT) images without access to raw projection data remains a significant difficulty in medical imaging, particularly when utilizing sharp or medium reconstruction kernels that generate high-frequency noise. This work introduces an innovative method that integrates quaternion mathematics with bilateral filtering to resolve this issue. The proposed Quaternion Bilateral Filter (QBF) effectively maintains anatomical structures and mitigates noise caused by the kernel by expressing CT scans in quaternion form, with the red, green, and blue channels encoded together. Compared to conventional methods that depend on raw data or grayscale filtering, our approach functions directly on reconstructed sharp kernel images. It converts them to mimic the quality of soft-kernel outputs, obtained with kernels such as B30f, using paired data from the same patients. The efficacy of the QBF is evidenced by both full-reference metrics (Structural Similarity Index Measure (SSIM), Peak Signal-to-Noise Ratio (PSNR), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE)) and no-reference perceptual metrics (Naturalness Image Quality Evaluator (NIQE), Blind Referenceless Image Spatial Quality Evaluator (BRISQUE), and Perception-based Image Quality Evaluator (PIQE)). The results indicate that the QBF demonstrates improved denoising efficacy compared to traditional Bilateral Filter (BF), Non-Local Means (NLM), wavelet, and Convolutional Neural Network (CNN)-based processing, achieving an SSIM of 0.96 and a PSNR of 36.3 on B50f reconstructions. Additionally, segmentation-based visual validation verifies that QBF-filtered outputs maintain essential structural details necessary for subsequent diagnostic tasks. This study emphasizes the importance of quaternion-based filtering as a lightweight, interpretable, and efficient substitute for deep learning models in post-reconstruction CT image enhancement.