l_p范数约束的去冲击干扰优化算法

l_p-norm regularization optimization of impulsive disturbance removal

为解决在冲击干扰下信号的恢复问题,提出了一种利用lp范数约束的优化算法。因为lp(0<p<1)范数约束的引入会导致提出的优化模型退化为难以求解的非凸优化问题,因此利用交替方向乘子法来有效解决该优化问题。文中分别利用迭代重加权最小二乘法和内点法求得了优化问题中对应优化变量的迭代方程,并将该算法用于图像增强。数值仿真结果说明了相比于lp-ADM算法,加权lp范数约束优化算法有更好的恢复性能。

This work addresses the signal recovery problem in the presence of impulsive disturbance utilizing lp-norm optimization.In doing so,the resultant optimization is difficult to solve,especially when 0<p<1,because it is nonconvex.In this work,the alternating direction method for multipliers steps is developed to eficiently obtain the solution from this optimization.In each step of the alternating direction method for multipliers,the corresponding solutions are respectively obtained by utilizing the iteratively reweighted least squares and interior-point approach.Numerical studies including an application of image enhancement demonstrate the superior performance of the proposed weighted estimation algorithms compared to the lp-ADM approach.