Compressive　sensing　(CS)　theory,　which　has　been　widely　used　in　magnetic　resonance　(MR)　image　processing,　indicates　that　a　sparse　signal　can　be　reconstructed　by　the　optimization　programming　process　from　non-adaptive　linear　projections.　Since　MR　Images　commonly　possess　a　blocky　structure　and　have　sparse　representations　under　certain　wavelet　bases,　total　variation　(TV)　and　wavelet　domain　norm　regularization　are　enforced　together　(TV-wavelet　Ll　method)　to　improve　the　recovery　accuracy.　However,　the　components　of　wavelet　coefficients　are　different:　low-frequency　components　of　an　image,　that　carry　the　main　energy　of　the　MR　image,　perform　a　decisive　impact　for　reconstruction　quality.　In　this　paper,　we　propose　a　TV　and　wavelet　L2-L1　model　(TVWL2-L1)　to　measure　the　low　frequency　wavelet　coefficients　with　2　norm　and　high　frequency　wavelet　coefficients　with　l(1)　norm.　We　present　two　methods　to　approach　this　problem　by　operator　splitting　algorithm　and　proximal　gradient　algorithm.　Experimental　results　demonstrate　that　our　method　can　obviously　improve　the　quality　of　MR　image　recovery　comparing　with　the　original　TV-wavelet　method.　(C)　2012　Elsevier　Inc.　All　rights　reserved.