Automatic balancing parameter selection for Tikhonov-TV regularization

Abstract This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such we consider regularizers consisting two terms that must balanced. Namely, a Tikhonov term guarantees the smoothness solution component, while total-variation (TV) regularizer promotes blockiness non-smooth component. A scalar parameter allows to balance between these and, hence, appropriately separate regularize components solution. proposes an efficient algorithm this regularization problem by alternating direction method multipliers (ADMM). Furthermore, novel for automatic choice balancing is introduced, using robust statistics. The proposed approach supported some theoretical analysis, numerical experiments concerned with different are presented validate parameter.