1) CS introduces a framework for simultaneous sensing and compression of big size vectors that applies in a range of applications including Optical Imaging and Synthetic Aperture Radar. 2) Total variation minimization, split Bregman, linearized Bregman and sparse reconstruction propose extremely efficient methods for solving optimization problems, which transform l₁-norm constrained problems into unconstrained problems by adding penalty term.. In the paper, the main principles of several algorithms are firstly introduced, then optimization iteration steps for algorithms are presented in detail. 3) Next, to research the performances of the algorithms in terms of the convergence and reconstruction precision, a series of numerical experiments for the above algorithms clearly show visual qualities of reconstructed images.4) we analyze the influence of the parameters u and g on iterative performances as well as the difficulties of controlling parameters, making clear the advantage of The Minimum total variation compared to other algorithms, and the low-complexity of Bregman .