Variational Bayes inference based segmentation algorithms for brain PET-CT images

Dual modality PET-CT imaging can provide aligned anatomical (CT) and functional (PET) images in a single scanning session, and has nowadays steadily replaced single modality PET imaging in clinical practice. The enormous number of PET-CT images produced in hospitals are currently analysed almost entirely through visual inspection on a slice-by-slice basis, which requires a high degree of skill and concentration, and is time-consuming, expensive, prone to operator bias, and unsuitable for the processing large-scale studies. Computer-aided diagnosis, where image segmentation is an essential step, would enable doctors and researchers to bypass these issues. However, most medical image segmentation methods are designed for single modality images. In this thesis, the automated segmentation of dual-modality brain PET-CT images has been comprehensively investigated by using variational learning techniques. Two novel statistical segmentation algorithms, namely the DE-VEM algorithm and PA-VEM algorithm, have been proposed to delineate brain PET-CT images into grey matter (GM), white matter (WM) and cerebrospinal fluid (CSF). In statistical image segmentation, voxel values are usually characterised by probabilistic models, whose parameters can be estimated by using the maximum likelihood estimation, and the optimal segmentation result is regarded as the one that maximises the posterior probability. Despite of their simplicity, statistical approaches intrinsically suffer from overfitting and local convergence. In variational Bayes inference, statistical model parameters are further assumed to be random variables to improve the model's flexibility. Instead of directly estimating the posterior probability, variational learning techniques use a variational distribution to approximate the posterior probability, and thus are able to overcome the drawback of overfitting. The most widely used variational learning technique is the variational expectation maximisation (VEM) algorithm. As a natural extension of the traditional expectation maximisation (EM) algorithm, the VEM algorithm is also a two-step iterative process and still faces the risk of being trapped in a local maximum and the difficulty of incorporating prior knowledge. Inspired by the fact that global optimisation techniques, such as the genetic algorithm, have been successfully applied to replace the EM algorithm in the maximum-likelihood estimation of probabilistic models, this research combines the differential evolution (DE) algorithm and VEM algorithm to solve the optimisation problem involved in the variational Bayes inference, and thus proposes the DE-VEM algorithm for brain PET -CT image segmentation. In this algorithm, the DE scheme is introduced to search a global solution and the VEM scheme is employed to perform a local search. Since DE is population-based global optimisation technique and has proven itself in a variety of applications with good, the DE­YEM algorithm has the potential to avoid local convergence. The proposed algorithm has been compared with the YEM algorithm and the segmentation function in the statistical parametric mapping (SPM, Version 2008) package in 21 clinical brain PET -CT images. My results show that the DE-YEM algorithm outperforms the other two algorithms and can produce accurate segmentation of brain PET-CT images. Meanwhile, to incorporate the prior anatomical information into the variational learning based brain image segmentation process, the probabilistic brain atlas is generated and used to guide the search of an optimal segmentation result through performing the YEM iteration. As a result, the probabilistic atlas based YEM (PA-YEM) algorithm is developed to allow each voxel to have an adaptable prior probability of belonging to each class. This algorithm has been compared to the segmentation functions in the SPM8 package and the EMS package, the DE-YEM algorithm, and the DEV algorithm in 21 clinical brain PET-CT images. My results demonstrate that the proposed PA-YEM algorithm can substantially improve the accuracy of segmenting brain PET -CT images. Although this research uses the brain PET -CT images as case studies, the theoretical outcomes are generic and can be extended to the segmentation of other dual-modality medical images. The future work in this area should be focused mainly on improving the computational efficiency of variational learning based image segmentation approaches