CAJ | 학술논문

在盲源分离和独立成分分析中，峭度是衡量随机信号非高斯性的常用对比准则，通过不同类型的算法对其进行优化，找到非高斯性极大值点，即实现了源信号的提取或分离。例如，基于峭度的快速不动点算法，它是一种收敛速度很快的算法。最近，Marc Castella等人提出了一类基于所谓“参考信号”的对比准则，以及对应的梯度最大化优化算法，这些算法具有很好的收敛性能。受其启发，文章以一种类似的方式将“参考信号”思想应用到峭度中，得到一种新颖的对比函数，并基于该新峭度对比函数，提出了一种新的快速不动点算法。与经典的基于峭度的快速不动点算法相比，该算法极大地提高了收敛速度，尤其是随着信号样值点数的增加，该算法的优势会更加明显。文章分析和证明了该新峭度对比函数的局部收敛性，给出了新算法的详细推导过程，仿真实验验证了该算法的性能，并与经典算法进行了比较分析。
재맹원분리화독립성분분석중，초도시형량수궤신호비고사성적상용대비준칙，통과불동류형적산법대기진행우화，조도비고사성겁대치점，즉실현료원신호적제취혹분리。례여，기우초도적쾌속불동점산법，타시일충수렴속도흔쾌적산법。최근，Marc Castella등인제출료일류기우소위“삼고신호”적대비준칙，이급대응적제도최대화우화산법，저사산법구유흔호적수렴성능。수기계발，문장이일충유사적방식장“삼고신호”사상응용도초도중，득도일충신영적대비함수，병기우해신초도대비함수，제출료일충신적쾌속불동점산법。여경전적기우초도적쾌속불동점산법상비，해산법겁대지제고료수렴속도，우기시수착신호양치점수적증가，해산법적우세회경가명현。문장분석화증명료해신초도대비함수적국부수렴성，급출료신산법적상세추도과정，방진실험험증료해산법적성능，병여경전산법진행료비교분석。
In the blind source separation (BSS)and independent component analysis (ICA),kurtosis is a common contrast measure for non-gaussianity of stochastic signals.The source signals can be extracted or recovered by using different optimiza-tion algorithms to find the non-gaussianity maximization points.For instance,the fast fixed-point algorithm based on kurtosis is a very classical one,which has very fast convergence speed.Recently,a family of so-called reference-based contrast criteria have been proposed by Marc Castella etc,and corresponding gradient maximization algorithms have also been proposed,which show very good performance.Inspired by them,the reference-based scheme is applied in kurtosis to construct a new kurtosis contrast function in a similar manner,based on which a novel fast fixed-point algorithm is proposed in this paper.Compared with the classical kurtosis-based fast fixed-point algorithm,this new algorithm is much more efficient in terms of computational speed,which is significantly apparent with large number of samples.The local consistency of this new contrast function is an-alyzed and proved,and the derivation of this new algorithm is also presented in detail.The performance of this new algorithm is validated through simulations,together with corresponding comparison and analysis.