A Fast Adaptive Parameter Estimation for Total Variation Image Restoration

Estimation of the regularization parameter, which strikes a balance between the data fidelity and regularity, is essential for successfully solving ill-posed image restoration problems. Based on the classical total variation (TV) model and prevalent alternating direction method of multipliers, we hammer out a fast algorithm being able to simultaneously estimate the regularization parameter and restore the degraded image. By applying variable splitting technique to both the regularization term and data fidelity term, we overcome the nondifferentiability of TV and achieve a closed form to update the regularization parameter in each iteration. The solution is guaranteed to satisfy Morozov's discrepancy principle. Furthermore, we present a convergence proof for the proposed algorithm on the premise of a variable regularization parameter. Experimental results demonstrate that the proposed algorithm is superior in speed and competitive in accuracy compared with several state-of-the-art methods. Besides, the proposed method can be smoothly extended to the multichannel image restoration.