【摘要】 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。更多还原

【Abstract】 Smoothed l0 norm algorithm(SL0) is a convex programming reconstruction algorithm based on approximate l0 norm. Compared with conventional algorithms, it has many advantages, such as the high estimation precision, the low calculation, no need for the sparsity of a signal and robust resistance to signal noises. However, the iterative direction is negative gradient direction, which has "notched effect", and the calculation of the iterative step length is complex. In this paper, the hyperbolic tangent function is used to approximate the l0 norm. And a new efficient algorithm named NSL0 is proposed based on smoothed l0 norm and the revised Newton method. It could get a further improvement in construction speed. The experimental results show that the NSL0 algorithm has great improvement in both convergence speed and the signal-to-noise ratio to the SL0 algorithm under the same experimental conditions.更多还原