Abstract: Image denoising based on total variation may cause‘staircase effect' while the noise is removed. Using the coupled gradient fidelity term can effectively restrain‘staircase effect'，but it makes edges obscured. I}his paper discussed the the way to detect smooth regions of an image. And three denoising methods with gradient fidelity term on smoothing region were proposed. Our methods can not only improve the denoising performance significantly, but also overcome ‘staircase effect' and preserve the edges. Numerical experiments demonstrate our models arc efficiency.

Key words: Denoising, Gradient fidelity, Smoothing region, Orientation-matching minimization