An　error　estimate　method　based　on　equalization　quantization　noise　model　was　proposed　for　non-uniform　quantization　noise　in　image　codec.　With　designed　equalization　matrix,　a　norm　constraint　which　could　enhance　the　quality　of　CS　recovery　significantly　was　shown.　Furthermore,　for　directional　textures　of　images,　a　multi-direction　operator　which　could　enhance　the　quality　of　CS　optimize　recovery　was　shown.　A　CS-based　JPEG　decoding　scheme　based　on　quantization　error　estimate　and　multi-direction　operator　was　also　presented,　and　experimental　evidence　exhibits　more　gains　over　CS　reconstruction　without　error　estimation　and　multi-direction　operator.