32.2 Linear Spectral Mixture Analysis for MRI

A fundamental task of MRI is tissue classification. Traditionally, it takes advantage of intervoxel spatial correlation to perform spatial domain-based classification by voxel membership assignment. In other words, a spatial domain-based classification technique performs no more than class labeling for data samples via a clustering or segmentation process. As a result, MR image voxels must be classified by hard decisions, that is, discrete decisions. Unfortunately, since many tissue substances in MR images may be indeed mixed by more than one tissue substance within a single voxel, it is more realistic and effective to classify an MR image voxel by soft decisions based on the proportion of each of these tissue substances present in the particular voxel. In the past, two mainstreams are investigated for such soft decisions, referred to as PVE. One is a parametric approach that makes use of a mixing model to estimate partial volumes of each of tissue substances present in a voxel, also referred to as a mixel (Choi et al., 1991; Santago and Gage, 1993; Laidlaw et al., 1998; Harris et al., 1999; Ruan et al., 2000; Shattuck et al., 2001; Leemput et al., 2003; Siadat and Soltanian-Zade, 2007; Klauschen et al., 2009). The other is a nonparametric approach, which uses FCM-based clustering techniques for the same purpose (Wells, III, et al., 1996; Pham and Prince, 1999; Ahmed et al., 2002; Liew and Yan, 2003; Siyal and Yu, 2005).

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