A variational image restoration with spatially varying noise

The noise in natural images sometimes changes according to imaging mechanism or local image information. This is called spatially varying noise. It is obvious that classical variational denoising algorithms such as the Rudin-Osher-Fatemi model are not suitable for this kind of noise. We propose a variational method to remove this spatially varying noise based on the estimation of local variance for a given image, such that high noise regions are smoothed meanwhile the textures and certain details in low noise regions are preserved. Moreover, we give the proof of existence of the minimizer of our proposed functional. The experimental results show visual improvement and high signal-to-noise ratio over other variational denoising models.