基追踪问题的近点算法及其应用研究

A proximal point algorithm of basis pursuit and its applications

基追踪问题具有广泛的应用背景,近年来得到了大量的关注和研究。近点算法是解决该问题的一种有效算法,其关键是子问题的求解,利用线性Bregman迭代的求解思想进行Lagrange对偶分析求解子问题,设计了一个新的迭代算法BP-PPA。与线性Bregman算法相比,BP-PPA可避免参数选取对模型的依赖,并用于非压缩感知的稀疏恢复问题求解。同时,为了提高新算法的收敛速度,进一步对新算法进行了Nestrove加速,得到了加速的BP-PPA算法。数值实验中,分别针对压缩感知中的稀疏信号恢复和非压缩感知模型,测试了参数选取对算法效率的影响,实验结果验证了新算法的有效性。

Basis pursuit has promising applications and becomes a hotspot research topic in recent years. The proximal point algorithm is an effective way for solving basis pursuit problems. We propose a new algorithm, which combines the proximal point algorithm and the idea of linearized Bregman algorithm to solve this problem under the Lagrange dual analysis. Compared with the original linearized Bregman algorithm, the proposed algorithm can avoid the dependency of parameter selection on the mod- el, so its application is beyond the compressed sensing problems. In order to accelerate the convergence speed of the new algorithm, every sub-problem is speeded up by Nestrove acceleration scheme. In the simulations on sparse recovery problems of both compressed sensing and non-compressed sensing, we test the influence of parameter selections on the algorithm＇s convergence, and the results demonstrate the advantage of this new algorithm.