Rectified subspace analysis of dynamic positron emission tomography

Subspace analysis is a popular method for multivariate data analysis and is closely related to factor analysis and principal component analysis (PCA). In the context of image processing (especially positron emission tomography), all data points are nonnegative and it is expected that both basis images and factors are nonnegative in order to obtain reasonable results. Recently the nonnegative matrix factorization (NMF) was introduced (D.D. Lee and H.S. Seung, 1999). It was demonstrated that the NMF gave parts-based representation and was useful in dynamic PET image analysis. We present a sequential EM algorithm for rectified subspace analysis (subspace in nonnegativity constraint) and apply it to dynamic PET image analysis. Experimental results show that our proposed method is useful in dynamic PET image analysis.