A partial differential equation variational approach for simultaneous image denoising and contrast enhancement

Reducing noise while enhancing contrast and preserving edges is one of the most fundamental operations of image processing. However, noise reduction and contrast enhancement are conflicting requests, thus it is difficult to realize these two requests at the same time. In this paper, we propose two novel models for simultaneous image denoising and contrast enhancement using partial difference equation variational approach. The first model is based on modification of the classical simultaneous model, the other is total variation based image restoration. Both models are found to be effective in reducing staircasing effect while suppressing the artifacts along with both the theoretical and empirical analyses. Specifically, we resort to the total variation minimization method for image denoising and the piecewise linear stretching function to perform contrast enhancement. This paper seeks to combine these two different procedures with the same equation in a principled way. For numerical implementation, the step size of finite difference is adaptively chosen according to the curvature, leading to fewer iteration steps and satisfactory image quality. Experimental results demonstrate significant improvement over widely used algorithms in both objective and subjective image quality both quantitatively and visually.