Correction for ambiguous solutions in factor analysis using a penalized least squares objective

Factor analysis is a powerful tool used for the analysis of dynamic studies. One of the major drawbacks of factor analysis for dynamic structures (FADS) is that the solution is not mathematically unique when only non-negativity constraints are used to determine of factors and factor coefficients. In this work, a method to correct for ambiguous FADS solutions has been developed. A non-ambiguous solution is obtained by using an algorithm which constructs and minimizes a new objective function. The usual objective function consists of a least squares term, which by minimization with non-negativity constraints forces agreement between the applied factor model and the measured data. In our method, this objective function is modified by adding a term that penalizes structures in the images of the factor coefficients which are, due to non-uniqueness effects, built from more than one physiological component. The technique was tested on computer simulations, an experimental canine cardiac study using ^99mTc-teboroxime, and a patient planar ^99mTc-MAG₃ renal study. The results are compared with the truth in computer simulations and with region of interest (ROI) measurements in the experimental studies