In　this　paper　a　new　two-dimensional　method　for　blind　image　restoration,　based　on　an　L1　regularization　cost　function　is　presented.　A　generalized　gradient　algorithm　is　proposed　by　using　a　weak　derivative　of　the　absolute　value　function　to　deal　with　the　non-differentiable　case.　Unlike　the　double　regularization　(DR)　approach,　the　proposed　method　uses　the　L1　estimation　and　is　suitable　for　blind　image　restoration　under　non-Guassian　noise　environments.　Compared　with　the　NAS-RIF　approach,　the　proposed　method　doesn＇t　require　the　image　object　with　a　known　support.　Experimental　results　show　that　the　proposed　algorithm　can　obtain　a　better　image　estimate　with　a　faster　speed　than　three　conventional　blind　image　restoration　algorithms.　©2010　IEEE.