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.