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The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.doi:10.4236/act.2012.13007 fatcat:5kyk6jzp4jgn3liuvrpkn3sbbq