分析了LCNN的約束項的物理意義，認為約束項λ是有監督學習的加速度，使得整個算法無論是學習矩陣還是獨立成分的求解效率都可達到O(n)。針對不同的λ和源信號、觀測信號對的不同特性，提出了4種快速LCNN算法，分析了靜態圖像獨立成分分析模型，建立了單像素內的獨立模型，并總結了其優勢。
關 鍵 詞 Helmholtz自由能; 獨立成分分析(ICA); Lagrange約束神經網絡; 單像素內獨立成分模型

Abstract The traditional independent component analysis is based on statistics mean of all aposteriori data and dismissed geometry. The classical lagrange constraint neural network (LCNN) employs Helmholtz free energy to unify supervised and unsupervised learning, and uses aprior and multi-sensing to solve independent components in one pixel, whose geometrical grain reached single pixel. The operations among pixels can be completely run parallelly. However, the constraints of classical LCNN bring ill-conditional matrix. In this paper, the real meaning of the constraints λ is discussed, four fast LCNN algorithms are proposed, the independent component (IC) models of still image is analyzed, and a new sub-pixel IC model is presented.
Key words Helmholtz free energy; independent component; lagrange constraint neural network; sub-pixel independent component model