Based on the compressive sensing,a novel algorithm is proposed to solve reconstruction problem under sparsity assumptions.Instead of estimating the reconstructed data through minimizing the objective function,the authors parameterize the problem as a linear combination of few elementary thresholding functions,which can be solved by calculating the linear weighting coefficients.It is to update the thresholding functions during the process of iteration.The advantage of this method is that the optimization problem only needs to be solved by calculating linear coefficients for each time.With the elementary thresholding functions satisfying certain constraints,a global convergence of the iterative algorithm is guaranteed.The synthetic and the field data results prove the effectiveness of the proposed algorithm. Based on the compressive sensing, a novel algorithm is proposed to solve reconstruction problem under sparsity assumptions. Instead of estimating the reconstructed data through minimizing the objective function, the authors parameterize the problem as a linear combination of few elementary thresholding functions, which can be solved by calculating the linear weighting coefficients .It is to update the thresholding functions during the process of iteration.The advantage of this method is that the the optimization of only needs be be solved by calculating linear coefficients for each time .With the elementary thresholding functions satisfying certain constraints, a global convergence of the iterative algorithm is guaranteed. The synthetic and the field data results prove the effectiveness of the proposed algorithm.