It　is　known　that,　the　compressive　sensing　theories　offered　the　possibilities　of　accurately　recon-structing　images　from　highly　undersampled　data　and　simultaneously　correcting　the　possible　noise.　It　is　also　known　that,　if　the　undersampled　data　is　corrupted　by　white　Gaussian　noise,　the　state-of-the-art　solver　RecPF　can　be　employed　successfully,　but　for　impulsive　noise,　it　is　not　quite　suitable.　As　a　remedy,　in　this　paper,　we　concentrate　on　the　impulsive　noise　case,　and　particularly　focus　on　the　cost　function　being　the　sum　of　a　total　variation　regularized　term,　an　l(1)-norm　regularized　term,　and　an　l(1)-norm　measured　data　fidelity　term.　However,　this　cost　function　cause　a　little　more　challenges　for　minimizing　because　of　these　non-differentiable　terms.　To　tackle　this　difficulty,　this　paper　presents　a　pair　of　efficient　algorithms　from　two　different　aspects:　(1)　employing　an　alternating　direction　method　of　multipliers　(ADMM)　to　solve　the　primal　problem　in　a　straightforward　way;　(2)　proposing　an　ADMM　to　the　dual　problem　whose　objective　function　contains　four　blocks　of　variables　and　three　blocks　of　non-differentiable　terms.　In　dual　cases,　a　symmetric　Gauss-Seidel　technique　is　employed　to　decompose　the　involved　bigger　subproblem　into　some　smaller　ones.　It　should　be　emphasized　that　the　most　remarkable　feature　of　our　proposed　algorithms　is　that　each　subproblem　is　easily　implementable　by　making　full　use　of　the　favorable　structures,　such　as　the　fast　Fourier　transforms,　the　proximal　mapping　and　the　Moreau　decomposition　of　ti-norm　function.　We　do　extensive　numerical　sim-ulations　using　some　magnetic　resonance　images　which　demonstrate　that　the　algorithm　based　on　dual　model　is　evidently　efficient.