A New Variational Approach for Multiplicative Noise and Blur Removal

This paper proposes a new variational model for joint multiplicative denoising and deblurring. It combines a total generalized variation filter (which has been proved to be able to reduce the blocky-effects by being aware of high-order smoothness) and shearlet transform (that effectively preserves anisotropic image features such as sharp edges, curves and so on). The new model takes the advantage of both regularizers since it is able to minimize the staircase effects while preserving sharp edges, textures and other fine image details. The existence and uniqueness of a solution to the proposed variational model is also discussed. The resulting energy functional is then solved by using alternating direction method of multipliers. Numerical experiments showing that the proposed model achieves satisfactory restoration results, both visually and quantitatively in handling the blur (motion, Gaussian, disk, and Moffat) and multiplicative noise (Gaussian, Gamma, or Rayleigh) reduction. A comparison with other recent methods in this field is provided as well. The proposed model can also be applied for restoring both single and multi-channel images contaminated with multiplicative noise, and permit cross-channel blurs when the underlying image has more than one channel. Numerical tests on color images are conducted to demonstrate the effectiveness of the proposed model.