In　order　to　relax　need　of　the　optimal　regularization　parameter　to　be　estimated,　a　cooperative　recurrent　neural　network　(CRNN)　algorithm　for　image　restoration　was　presented　by　solving　a　generalized　least　absolute　deviation　(　GLAD)　problem.　This　paper　proposes　a　fast　algorithm　for　solving　a　constrained　l(1)-norm　problem　which　contains　the　GLAD　problem　as　its　special　case.　The　proposed　iterative　algorithm　is　guaranteed　to　converge　globally　to　an　optimal　estimate　under　a　fixed　step　length.　Compared　with　the　CRNN　algorithm　being　continuous　time,　the　proposed　iterative　algorithm　has　a　fast　convergence　speed.　Illustrative　examples　with　application　to　image　restoration　show　that　the　proposed　iterative　algorithm　has　a　much　faster　convergence　rate　than　the　CRNN　algorithm.