Sparse non-negative matrix factorizations for ultrasound factor analysis

Factor analysis is a powerful tool used for the analysis of dynamic studies. One of the major drawbacks of Factor Analysis of Dynamic Structures (FADS) is that the solution is not mathematically unique when only non-negativity constraints are used to determine factors and factor coefficients. In this paper, we introduce a novel method to correct FADS solutions by constructing and minimizing a new objective function. The method is improved from non-negative matrix factorizations (NMFs) algorithm by adding a sparse constraint that penalizes multiple components in the images of the factor coefficients. The technique is tested on computer simulations, and a patient ultrasound liver study. The results show that the method works well in comparison to the truth in computer simulations and to region of interest (ROI) measurements in the experimental studies.