Combination of hybrid median filter and total variation minimisation for medical X-ray image restoration

X-ray image restoration is a difficult problem aimed at improving image quality for visual inspection. Preservation of edges and relevant image information are important for the diagnosis of diseases by physicians or radiologists. In this research, the authors combined a hybrid median filter (HMF) and total variation (TV) minimisation to restore medical X-ray images. A standard TV minimisation preserves the edges or boundaries of the reconstructed image but also includes false edges. A modified HMF was employed on a Lagrange multiplier associated with a gradient constraint to remove these false edges during the multiplier update. The TV minimisation unconstrained problem was transformed into a constrained form. An augmented Lagrangian method with a variable penalty term was used to handle the constraints in the form for faster convergence, and the alternative direction method solved the subproblems iteratively. The proposed techniques provide improved convergence speed and restore good quality medical X-ray images to remove false edges and the staircase effect.