CAJ | 학술논문

针对欠定线性方程组稀疏解的求解问题,文中提出两个改进的迭代重加权最小范数解算法(IRMNS)及一个光滑的0函数算法.其中,第一个算法基于 q(q∈(0,1])范数提出的,当q较小的时候,算法可以增强恢复稀疏解的能力;第二个算法是直接由0范数最小化问题提出的,它可以看做是第一个算法在q =0时的拓展;第三个算法是通过用一个光滑函数来近似0范数从而将原问题进行转化求解的.数值例子表明这三种算法都是快速有效的.
침대흠정선성방정조희소해적구해문제,문중제출량개개진적질대중가권최소범수해산법(IRMNS)급일개광활적0함수산법.기중,제일개산법기우 q(q∈(0,1])범수제출적,당q교소적시후,산법가이증강회복희소해적능력;제이개산법시직접유0범수최소화문제제출적,타가이간주시제일개산법재q =0시적탁전;제삼개산법시통과용일개광활함수래근사0범수종이장원문제진행전화구해적.수치례자표명저삼충산법도시쾌속유효적.
In this paper, two improved iteratively re-weighted minimum norm solution (IRMNS) algorithms and a smoothed 0 function algorithm are proposed for the recovery of sparse solutions of under-determined linear systems. The first algorithm is base on q-minimization for q ∈(0, 1]. It can substantially enhance the ability to reconstruct sparse solutions when q is small. The second improved algorithm is derived directly from the 0 norm minimization. It can be regarded as an extension of the first one to the case where q=0. The third algorithm uses a smoothed 0 function to approximate the 0 norm. Numerical experiments show that all of the algorithms are fast and e?cient.