Partial volume estimation of magnetic resonance image using linear spectral mixing analysis

Because of the strength in providing high contrasts of soft tissues Magnetic Resonance Imaging (MRI) has been an important medical modality in diagnosis of tissue characterization such as tissue classification and analysis as well as quantitative imaging such as partial volume estimation. Over the past years, numerous techniques have been developed for MRI and can be roughly categorized into two principal approaches. One is a structural approach which is primarily based on spatial correlation among MR image pixels, referred to as voxels. This type of approach is considered as a spatial domain-based clustering technique, examples include edge detection, region growing, segmentation etc. As a result, a structural approach is generally used for tissue characterization such as segmentation, classification, texture analysis. The other is a statistical approach which is essentially a parametric technique based on Finite Gaussian Mixture (FGM) models coupled with Markov Random Field (MRF) to capture intra-voxel correlation. Consequently, this approach is mainly used for partial volume estimation. Unfortunately, both approaches suffer from certain drawbacks, some of which are particularly severe, for example, computational complexity, invalid assumption such as Gaussianity and limited generalizability such as extension to tissue detection. In order to address these issues, this dissertation develops a rather different and completely new approach which is solely based on intra-voxel correlation without using an MRF model. It is derived from a hyperspectral imaging point of view where Linear Spectral Mixture Analysis (LSMA) is used to replace the FGM model-based analysis to perform spectral unmixing where LSMA-unmixed abundance fractions can be interpreted as partial volume estimates. Such an LSMA-based approach can be considered as a third approach and is believed to be the first of its kind which has never been explored in terms of LSMA's framework in the literature. However, in order for a hyperspectral imaging technique to be applicable to MRI, a key issue needed to be addressed is the limited spectral information provided by a voxel using only a small number of image sequences, namely, T1, T2 and PD (photon density). To resolve this issue two major techniques are developed to expand spectral information in this dissertation. One is to use Band Expansion Process (BEP) to expand spectral dimensionality via a nonlinear function so that an original (T1,T2,PD)-voxel can be expanded to a multi-dimensional pixel vector with its dimensionality greater than 3 with which LSMA can work more effectively. The other is to introduce a nonlinear kernel into LSMA, referred to as kernel-based LSMA (K-LSMA) which can make nonlinear decisions to cope with linear non-separability problems caused by insufficient spectral information. Furthermore, in order to further extend LSMA's unmixed capability, a kernel-based unsupervised LSMA (K-ULSMA) is also developed for tissue detection which generally cannot be accomplished by structural and statistical approaches. Finally, in order to perform quantitative analysis, two evaluation tools are further developed in this dissertation, 3D Receiver Operating Characteristics (3D ROC) analysis for partial volume estimation and 2D Tanimoto Index Curve (2D TIC) for soft-decision made classification. Specifically, 2D TIC is a newly developed concept and has never been explored and reported in the literature.