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在稀疏信息处理中,l0范数优化问题通常转化为l1范数优化问题来求解。但l1范数优化问题存在一些不足。为寻找一种更有效的求稀疏解的算法,首先构造一个新的收缩算子,其次证明该收缩算子是某非凸函数的邻近算子。然后用该非凸函数替代l0-范数,对新的优化问题用向前-向后分裂方法得到对应的迭代阈值算法-迭代分式阈值算法(IFTA)。仿真实验表明该算法(IFTA)在稀疏信号重构和高维变量选择中均有良好的表现。
In sparse information processing, l0 norm optimization problems usually translate into l1 norm optimization problems to solve. However, there are some shortcomings in the optimization of l1 norm. In order to find a more efficient algorithm for finding sparse solutions, we first construct a new contraction operator and secondly prove that the contraction operator is a neighboring operator of a non-convex function. Then the non-convex function is used to replace the l0-norm, and the corresponding iterative threshold algorithm - Iterative Fractional Threshold Algorithm (IFTA) is obtained by using the forward-backward splitting method for the new optimization problem. Simulation results show that this algorithm (IFTA) performs well in sparse signal reconstruction and high-dimensional variable selection.