Geometrical Method Using Simplicial Cones for Overdetermined Nonnegative Blind Source Separation: Application to Real PET Images

This paper presents a geometrical method for solving the overdetermined Nonnegative Blind Source Separation (N-BSS) problem. Considering each column of the mixed data as a point in the data space, we develop a Simplicial Cone Shrinking Algorithm for Unmixing Nonnegative Sources (SCSA-UNS). The proposed method estimates the mixing matrix and the sources by fitting a simplicial cone to the scatter plot of the mixed data. It requires weak assumption on the sources distribution, in particular the independence of the different sources is not necessary. Simulations on synthetic data show that SCSA-UNS outperforms other existing geometrical methods in noiseless case. Experiment on real Dynamic Positon Emission Tomography (PET) images illustrates the efficiency of the proposed method.