空間模型與時空模型於醫學影像分析的研究(2/2)

In medical image studies, the image of a subject's internal section generally shows spatially nonstationary features. How to appropriately specify a nonstationary covariance function for inherent spatial correlation to reconstruct the underlying image of the internal section is an intractable problem. Compared the resulting image with normal images, how to detect the differences among them is one of main goals. Moreover, monitoring the changes of images of a subject's internal sections over time is also a concerned issue. For such a longitudinal or a repeated medical imaging study, a specification of a suitable nonstationary spatiotemporal covariance structure is essential but is expected to be challenging in a modeling procedure. In this proposal, we attempt to propose a spatial and temporal model-based approach to decompose the observed imagingdata into signals and noises, where signals include a fixed effect and a random effect. We consider a linear combination of covariates for the fixed effect and use a nonparametric technique based on some basis functions to model the underlying spatiotemporal covariance processes, where separable and nonseparable correlation functions and the number of basis functions will be investigated. The proposed idea does not require specifying a parametric covariance structure and can be applied to massive data sets without handling the computational issue of high-dimensional inverse matrices. As a result, it is more flexible than the conventional methods. To avoid over-fitting the image data, we will develop a model selection criterion from a prediction perspective to identify a suitable subset of covariates and simultaneously determine the number of basis functions. After modeling (or, denoising), image segmentation and feature extraction will be studied. Statistical inferences associated with the proposed methodology will be justified in theories and via simulations. Finally, some real data examples regarding medical images will be analyzed for illustration.