Total variation minimizing methods have known great success in image denoizing. Although edge sharpness is well preserved by these methods, important information like textures or small details is often removed in the process of denoizing. We propose a novel denoizing model which better preserves fine scale features. In our model, a set of local constraints are imposed to keep local variance of the noise at certain scale within its proper bounds. Each constraint corresponds to a certain scale of dyadic region of image and therefore the Lagrange multiplier in the model is space and scale adaptive, which can control the extent of denoizing over dyadic image regions. We characterize the local constraints by wavelet coefficients in order to transform the model into wavelet domain, and then give the solution and algorithm of the proposed model. Finally, we display some numerical experiments to demonstrate that the proposed model can preserve fine scale features effectively in the process of denoizing and the algorithm is quite practical.