科研之友
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摘要
We study the L-2-L-1/2 minimization problem arising from compressive sensing. We first derive an equivalent nonsmooth equation to the first order necessary condition of the problem. Based on this equation, we construct a descent direction for the objective function and then develop a gradient based method to solve the problem. The method is very easy to implement. A good property of the method is that the generated sequence of the function evaluations is decreasing. Under mild conditions, we prove the global convergence of the method. Our preliminary numerical results show that the proposed method is practically effective.
