Medical image enhancement through Klein–Gordon model with advanced differential operators

Image enhancement in medicine is crucial for diagnosing anatomical structures like tissues, organs, bones, and tumors. Insufficient lighting, incorrect settings, sensor constraints, excessive exposure, noise, patient motion, technical artifacts, and poor post–processing lead to low contrast and distorted noise interference. Consequently, the processes of diagnosis and decision-making is a challenges for medical professionals. The proposed work introduces a novel method using the Klein–Gordon equation to model image intensity as a scalar field, improving propagation, reducing noise, and maintaining edge sharpness. The Grunwald-Letnikov fractional derivative detects subtle edges while balancing smoothing and enhancement, preserving internal structure. Hausdorff fractal derivative significantly influence low-contrast images by improving local contrast and preserving details. The proposed method’s effectiveness is shown through assessments using no-reference image quality metrics BRISQUE and NIQE. The technique uses Chest X-ray, Dental X-ray, SARS-COV-CT Scan, and brain MRI results in BRISQUE and NIQE values, revealing significant visual enhancements over other methods.