The problem of compressive-sensing(CS)L2-L1-TV reconstruction of magnetic resonance(MR)scans from undersampled k-space data has been addressed in numerous studies.However,the regularization parameters in models of CS L2-L1-TV reconstruction are rarely studied.Once the regularization parameters are given,the solution for an MR reconstruction model is fixed and is less effective in the case of strong noise.To overcome this shortcoming,we present a new alternating formulation to replace the standard L2-L1-TV reconstruction model.We prove that this new formulation is equivalent to the standard one in some conditions.A weighted-average alternating minimization method is proposed based on this new formulation and a convergence analysis of the method is carried out.The advantages of and the motivation for the proposed alternating formulation are explained.Experimental results demonstrate that the proposed formulation yields better reconstruction results in the case of strong noise and can improve image reconstruction via flexible parameter selection.