TV-Wavelet-L1(TVWL1)model　which　consists　of　total-variation　(TV)　and　wavelet　regularization　has　great　capability　in　image　reconstruction.　However,　traditional　algorithms　solving　the　TVWL1　model　for　image　reconstruction　ignore　the　way　of　synthesis/analysis　sparse　representation.　A　new　image　reconstruction　algorithm　is　thus　proposed　to　solve　TVWL1,　where　the　original　signal　reconstruction　problem　is　decomposed　into　multiple　much　simpler　sub-problems　which　can　be　solved　alternately.　In　addition,　the　analysis　sparse　representation　is　considered　in　a　sub-problem.　Experimental　results　demonstrate　that　the　proposed　algorithm　can　obviously　improve　both　objective　and　subjective　qualities　of　reconstruction　images　compared　with　the　existing　algorithms.