Face recognition using independent component analysis (ICA)
For your data set of images, first vectorize the images by raster scanning them, and making them vectors. Thus, say you have $M$ images, each of size 64*64 pixels. Then the total number of pixels per image is $N=64^2$, which means $N=4096$. Now, you have an image matrix of size $M\text{x}N$. 

For this image matrix, what you want to do is find the $M$ independent components, of again, length $N$. In other words, you want to decompose this set of images into another set of images, except those images make up the independent components of the original faces. (Similar to eigen-faces, but different). 

To answer your question about the mixture, the set of faces that you start with is the mixture. In other words, the set of faces that you have, is assumed to be a mixture of independent faces that you are trying to find. 

ICA will find those independent features for you, and for natural images, independent components turn out to be features with extremely high kurtosis, namely, the edges.