基于改进平滑L0算法的图像重构

Image reconstruction based on improved Smoothing L0 algorithm

零范数平滑算法(SL0算法)中采用的最速下降法存在“锯齿现象”,在迭代后期步长减小、收敛速度慢,针对此问题文中提出一种改进SL0算法的压缩感知重构算法。该算法首先采用优化的高斯函数作为平滑函数提高重构精度,然后引入拟牛顿法以提高收敛速度。在对图像的重构实验中,通过不同算法对图像的重构误差、峰值信噪比、迭代时间等参数之间的对比结果表明,相比较标准的SL0算法和其他同类算法,改进的ONSL0算法在重构精度和收敛速度方面均有所提高,也证明了该算法的可行性及有效性。

In the Smoothing L0 algorithm(SL0 algorithm),the steepest descent method has“sawtooth phenomenon”.In the late iteration stage,the step size decreases and the convergence speed is slow.In order to solve this problem,an improved SL0 algorithm for compressed sensing reconstruction is proposed in this paper.The algorithm first uses the optimized Gauss function as a smoothing function to improve the reconstruction precision,and then the quasi Newton method is introduced to improve the convergence speed.In the experiment of image reconstruction,through comparing parameters about image reconstruction error,peak signal-to-noise ratio and the iteration time in different algorithms.The results show that compared with the standard SL0 algorithm and other algorithms,the improved ONSL0 algorithm improves the reconstruction precision and speed of convergence in the reconstruction,and the effectiveness and feasibility of the algorithm are proved.