College of Geo- Exploration Science and Technology��Jilin University��Changchun 130026��China

Based on the compressive sensing��a novel algorithm is proposed to solve reconstruction problem un- der 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 re- sults prove the effectiveness of the proposed algorithm��