In this paper, we consider the $\ell_0$ minimization problem whose objective function is the sum of $\ell_0$-norm and convex differentiable function. A variable metric type method which combines the PIHT method and the skill in quasi-newton method, named variable metric extrapolation proximal iterative hard thresholding (VMEPIHT) method, is proposed. Then we analyze its convergence, linear convergence rate and superlinear convergence rate under appropriate assumptions. Finally, we conduct numerical experiments on compressive sensing problem and CT image reconstruction problem to confirm VMPIHT method's efficiency, compared with other state-of-art methods.

翻译：在本文中,我们考虑的是美元=0美元最小化问题,其客观功能是 $\ ell_ 0$norm 和 convex 可区分功能。一种可变的计量方法,将PIHT 方法与准新通方法的技巧结合起来,称为可变的指数外推法(VMEPIHT ) 方法。然后我们根据适当的假设分析其趋同率、线性趋同率和超线性线性趋同率。最后,我们对压缩感测问题和CT图像重建问题进行数字实验,以确认VMPIHT 方法与其他最新方法相比的效率。