Image De-noising by Bayesian Regression

We present a kernel based approach for image de-noising in the spatial domain. The crux of evaluation for the kernel weights is addressed by a Bayesian regression. This approach introduces an adaptive filter, well preserving edges and thin structures in the image. The hyper-parameters in the model as well as the predictive distribution functions are estimated through an efficient iterative scheme. We evaluate our method on common test images, contaminated by white Gaussian noise. Qualitative results show the capability of our method to smooth out the noise while preserving the edges and fine texture. Quantitative comparison with the celebrated total variation (TV) and several wavelet methods ranks our approach among state-of-the-art denoising algorithms. Further advantages of our method include the capability of direct and simple integration of the noise PDF into the de-noising framework. The suggested method is fully automatic and can equally be applied to other regression problems.