In this paper, we present a simple yet effective image deblurring method to produce ringing-free deblurred images. Our work is inspired by the observation that large-scale deblurring ringing artifacts are measurable through a multi-resolution pyramid of low-pass filtering of the blurred-deblurred image pair. We propose to model such a quantification as a convex cost function and minimize it directly in the deblurring process in order to reduce ringing regardless of its cause. An efficient primal-dual algorithm is proposed as a solution to this optimization problem. Since the regularization is more biased toward ringing patterns, the details of the reconstructed image are prevented from over-smoothing. An inevitable source of ringing is sensor saturation which can be detected costlessly contrary to most other sources of ringing. However, dealing with the saturation effect in deblurring introduces a non-linear operator in optimization problem. In this paper, we also introduce a linear approximation as a solution to handling saturation in the proposed deblurring method. As a result of these steps, we significantly enhance the quality of the deblurred images. Experimental results and quantitative evaluations demonstrate that the proposed method performs favorably against state-of-the-art image deblurring methods.