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SL0算法是一种基于近似L0范数估计的凸规划迭代重建算法。与传统的重建算法相比,其估计精度高、计算量低;不需已知信号稀疏度,而且对噪声变化不是很敏感。但其迭代方向为负梯度方向,存在“锯齿效应”;迭代步长计算复杂。本文首先采用双曲正切函数来近似L0范数,然后结合修正牛顿法提出一种更快速高效的重建算法NSL0。实验结果表明,在相同的测试条件下,NSL0算法在收敛速度和信噪比方面都有了很大提高。
SL0 algorithm is a convex programming iterative reconstruction algorithm based on approximate L0 norm estimation. Compared with the traditional reconstruction algorithm, it has high estimation accuracy and low computational complexity. It does not need to know the signal sparsity and is not sensitive to the change of noise. However, the direction of iteration is negative gradient direction, there is “sawtooth effect ”; calculation of iterative step size is complicated. In this paper, we first use the hyperbolic tangent function to approximate the L0 norm and then propose a faster and more efficient reconstruction algorithm NSL0 based on the modified Newton method. Experimental results show that under the same test conditions, the NSL0 algorithm has a great improvement in convergence rate and signal-to-noise ratio.