This　paper　proposes　a　discrete-time　learning　algorithm　for　fast　image　restoration　using　a　novel　L2-norm　noise　constrained　estimation.　The　noise　constrained　estimation　approach　can　relax　the　need　of　the　optimal　regularization　parameter　to　be　estimated.　Performance　analysis　shows　that　the　proposed　algorithm　can　converge　globally　to　a　robust　optimal　weight　vector.　Compared　with　the　cooperative　neural　fusion　(CNF)　algorithm　minimizing　L1-norm　estimation,　the　proposed　algorithm　only　needs　O(N)　multiplication　operationper　iteration,　instead　of　O(N2)　multiplication　operation　required　by　the　CNF　algorithm.　Moreover,　the　proposed　fusion　approach　overcomes　the　difficulty　of　estimating　the　noise　error　set　in　the　CNF　approach.　Simulation　results　show　by　comparison　that　under　the　non-optimal　regularization　parameter,　the　proposed　algorithm　can　obtain　a　better　restored　estimate　in　Gaussian　mixture　noise　and　can　run　much　faster　compared　to　the　CNF　algorithm.　©　2016　Elsevier　B.V.