Texture Preserving Image Restoration with Dyadic Bounded Mean Oscillating Constraints

In this letter, we first propose an image restoration model with dyadic bounded mean oscillating (BMO) constraints to recover some clear texture from noisy data. The existence and uniqueness of the solution are discussed. The model is transformed into wavelet domain and then solved by dual Uzawa method. Each Lagrange multiplier of the discretized model corresponds to a certain scale of dyadic region of the image. Thus, the Lagrange multipliers are space adaptive and can control the extent of denoising over dyadic image regions. On the basis of this model, we propose a total variation (TV) based texture preserving denoising model. Finally, we display some numerical experiments to show the convergence of the algorithm and the validity of the proposed models.