A lot of discussions were made about solving the model of 1, morm minimization in the seismic inverse problem in paper [1] and [2]. But some strong conditions should be satisfied for the descent method in [1], A new modified algorithm presented in this paper can be implemented only when the matrix A is full rank for rows. So the new method has generality. Moreover we have modified the choice of the step factor, and the convergent speed is accelerated.
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