Application of image processing technology based on quaternion in medical image reconstruction

High-quality medical imaging is essential for accurate lesion detection and diagnostic precision in modern smart healthcare systems. Traditional reconstruction techniques, especially in optical tomography and CT imaging, often suffer from significant noise and loss of structural detail, severely affecting image usability. To overcome these limitations, this study proposes an iterative medical image reconstruction algorithm based on quaternion algebra, which maps pixel grayscale values and spatial relationships into a hypercomplex domain for enhanced denoising and 3D feature preservation. Experimental evaluation on multi-part CT datasets under three levels of Gaussian noise shows that the proposed method increases the peak signal-to-noise ratio (PSNR) by up to 4.7 dB, achieves a structural similarity index (SSIM) of 0.95, and yields a gradient similarity metric (GSM) improvement of 0.07 over traditional Fourier and total variation methods. In addition, average processing time is reduced to 2.3 seconds per image, supporting real-time clinical deployment. Subjective visual assessments further confirm clearer tissue boundaries and improved anatomical texture continuity. This study demonstrates the potential of quaternion-based models in optical imaging enhancement and lays a foundational framework for integrating hypercomplex mathematics into smart medical diagnostics and decision-making.