Linear dimension reduction of sequences of medical images: III. Factor analysis in signal space

A method is presented for improving the precision of factor analysis by utilizing physiological information. The first step is an optimal linear dimension reduction, whereby the data are projected onto a low-dimensional signal space. Then principal component analysis is performed in the signal space rather than in the entire data space. This improves the precision of the principal components. Unlike ordinary principal component analysis, the present method is not degraded when the time intervals are subdivided, provided that the signal space is correct. Alternatively, but with identical results, the covariance matrix can be calculated from the whole data space. The covariance matrix is then transformed and principal component analysis is performed in either a low-rank matrix or a low-dimensional submatrix instead of in the whole covariance matrix. Factor analysis using the intersection method with a theory space may be improved by employing the present method. In simulations based on a [11C]flumazenil study with 27 frames, the proposed method required only 58 per cent of the radioactivity to produce the same precision as the intersection method and only 27 per cent when compared to ordinary principal component analysis.