Variational denoising of partly textured images

The Rudin–Osher–Fatemi model is a widely used variational denoising algorithm which favors piecewise constant solutions. Although edge sharpness and location are well preserved, some local features such as textures and small details are often diminished with noise simultaneously. This paper aims to better preserve these local features using a similar variational framework. We introduce a texture detecting function according to the derivatives of the noisy textured image. Then this function is used to construct a spatially adaptive fidelity term, which adjusts the denoising extent in terms of the local features. Numerical results show that our method is superior to the Rudin–Osher–Fatemi model in both signal-to-noise ratio and visual quality. Moreover, part of our results are also compared with other state-of-the-art methods including a variational method and a non local means filter. The comparison shows that our method is competitive with these two methods in restoration quality but is much faster.