增广Lagrange函数优化算法在稀疏信号重构问题中的应用

Application of Augmented Lagrange Optimization Algorithm to the Sparse Signal Reconstruction Problem

针对稀疏信号恢复的lp优化模型(0<p≤1),提出了一种可行稳健的增广Lagrange函数优化算法。该算法通过构造精确罚函数的方法,设置有限的增广因子参数,有效地避免了类似于传统FOCUSS迭代算法中出现的计算病态性问题,从而极大提高了信号恢复的精确度。为解决大规模的信号重构问题,还引入了共轭梯度法,以促进算法加速收敛。最后,仿真结果表明,改进型的增广Lagrange函数优化算法较大程度提升了稀疏信号重构的能力。

To solve the problem of finding sparse solutions from lp optimization model（0p≤1）,this paper presented a kind of novel robust approach based on the augmented Lagrange optimization algorithm.This method introduces precise penalty function by setting limited value of augment factor to enhance the precision of signal recovery,which also avoids the problem of ill-condition computation happened in traditional FOCUSS algorithm.For dealing with large scale problem,Conjugate Gradient method was cooperated with the augmented Lagrange optimization algorithm to accelerate the convergence speed.Finally,computer simulations illustrate the performance on strengthening the recovery ability of signal.