Abstract: Endmember extraction is very important in mixed spectral analysis,which aims to identify the pure source signal from the mixture.In the past decade,many algorithms have been proposed to perform this estimation.One commonly used assumption is that all the endmembers have pure pixel representation in the scene.When such pixels are absent,these algorithms can only return certain pixels that are close to the real endmembers.To overcome this problem,we present a pure spectral calculation method without the pure pixel assumption for hyperspectral image analysis.The method is based on the alternative least square optimization,for its flexibility in containing several constraints for abundance and spectral,which refers to nonnegative,equality,closure,normalization and simplex volume constraints.There are other three problems are exploited: First,the traditional endmember algorithms are used for initialization;Second,spatial redundancy reduction is included in the preprocess procedure.The experimental results based on synthetic toy example and Cuprite mine area hyperspectral scene demonstrate that the proposed method can handle the pure pixels absent problem very well.