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.