摘要
针对一类可分的稀疏性度量函数,利用梯度分解技术给出了稀疏信号重构的拟牛顿算法。进一步研究表明,基于再加权最小2 范数的FOCUSS算法以及基于p 范数的正则化FOCUSS算法都是拟牛顿算法的特例。由此导出了可用于稀疏成份分析的广义正则化FOCUSS算法,并证明了该算法的收敛性。数值结果表明广义FO CUSS算法收敛到局部极小点,并且在迭代初值较为准确时能找到最合理的稀疏解。
For a class of separable sparsity measures, a quasi-Newton algorithm is developed based on gradient factorization for the purpose of sparse signal reconstruction. With detailed analysis, it is shown that the re-weighted minimum 2-norm based focal undetermined system solver (FOCUSS) algorithm and p-norm based regularized FOCUSS are special cases of the quasi-Newton algorithm. On this basis, a generalized version of regularized FOCUSS algorithm applicable to sparse component analysis is derived, and its convergence is subsequently proved. In the end, numeric results indicate that the generalized FOCUSS algorithm converges to local minima, and the most reasonable solution can be found when the initial value is relatively correct.
出处
《系统工程与电子技术》
EI
CSCD
北大核心
2005年第5期922-925,共4页
Systems Engineering and Electronics
关键词
稀疏成份分析
可分性度量
正则化
收敛性
sparse component analysis
separable measures
regularization
convergence
