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Image deblurring is an ill-posed linear inverse problem. Most traditional algorithms suffer from severe ringing artifacts. Recent approaches handle this issue by regularization techniques based on assumed image prior models. This paper presents a new method to reduce the ringing artifacts, without introducing any image prior models. For this purpose, we revisit the deblurring problem, using a probabilistic graph to model the image formation process. We establish the link between iterative back-projection and belief propagation and show that the ringing artifacts are caused by error propagation. Based on these analysis, we introduce a method to measure the variance of an estimation image and further propose an error-variance aware deblurring algorithm. Experimental results demonstrate that the proposed algorithm is very effective in suppressing the ringing artifacts.