In　this　paper,　we　give　an　analytical　model　of　the　compression　error　of　down-sampled　compression　based　on　wavelet　transform,　which　explains　why　down-sampling　before　compression　can　improve　coding　performance.　And　we　approximate　the　missing　details　due　to　down-sampling　and　compression　by　using　the　linear　combination　of　a　set　of　basis　vectors　with　L-1　norm.　Then　we　propose　a　down-sampled　and　high　frequency　information　approximated　coding　scheme　and　apply　it　to　natural　images,　and　achieve　gains　of　both　subjective　quality　and　objective　quality　compared　with　JPEG2000.　(C)　2011　Elsevier　B.V.　All　rights　reserved.