# Factor analysis of dynamic PET images

Intrinsic tissue heterogeneity and partial volume effect lead to image voxel time-activity curves that are a mixture of time-activity curves of pure homogeneous regions of tissue and blood. Factor analysis of dynamic data is a mathematical technique that aims to automatically resolve the true time-activity curves (Di Paola et al., 1982; Geckle and Szabo, 1992), helping in tissue segmentation, spill-over correction (Lee et al., 2005; Millet et al., 2012), obtaining image-derived input function (Wu et al., 1995; Ahn et al., 2000; Schiepers et al., 2008), and computation of parametric images (Tsartsalis et al., 2018).

The dynamic data is transformed to obtain key temporal components, and factor analysis fits a linear combination of selected components to the dynamic data. Typical problems in factor analysis, when applied to noisy data, include the high computational burden of the optimization process, and non-uniqueness of the results unless some constraints are set (Sitek et al., 2002).

## Non-negative matrix factorization

One obvious constraint that should be applied is non-negativity; non-negative matrix factorization (NMF, or sometimes NNMF, or non-negative matrix approximation, or self modeling curve resolution) (Lawton & Sylvestre, 1971; Paatero & Tapper, 1994; Paatero, 1997; Lee DD & Seung, 1999 and 2001; Li et al., 2014) has been shown to provide more robust segmentation of tissue and blood components than factor analysis or cluster analysis in dynamic PET (Lee JS et al., 2001a and 2001b; Kim et al., 2001; Choi et al., 2002; Ahn et al., 2004; Bödvarsson B et al., 2006 and 2007; Hwang et al., 2009; Schulz et al., 2012; Mu et al., 2013; Kopriva et al., 2017). NMF has not been successful in some PET applications (Zanotti-Fregonara et al., 2009).

NMF can be used as part of feature extraction methods in diagnostics, for example in FDG studies of Alzheimer’s disease (Segovia et al., 2016). The use of algorithms related to NMF are also used in PET image reconstruction.

## See also:

- Image filtering
- Image cluster analysis
- Spectral analysis
- Tools for processing image data
- Calculating parametric images
- NMF: DTU Toolbox

## References:

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Tags: Image, Factor analysis, IDIF

Created at: 2017-02-16

Updated at: 2018-12-06

Written by: Vesa Oikonen