In　this　paper　we　propose　a　novel　regularization　method　for　robust　image　reconstruction　against　noise,　based　on　convex　combination　of　the　least　squares　and　least　absolute　deviations.　Unlike　conventional　regularization　methods　with　an　assumption　of　Guaussian　noise,　the　proposed　regularization　method　can　deal　with　Gaussian　noise　and　non-Gaussian　noise.　To　overcome　difficulty　of　the　non-smooth　objective　function,　we　develop　an　efficient　sub-gradient　algorithm.　Computed　examples　with　an　application　to　MR　images　show　that　the　proposed　subgradient　algorithm　can　give　better　reconstruction　quality　than　the　conventional　reconstruction　regularization　algorithms　in　various　noise.　©　2015　IEEE.