統計方法及推論研討會

中央研究院統計科學研究所

國 立 台 灣 大 學 數 學 系

協辦單位:國家科學委員會數學研究推動中心

時　 間：2000年03月09日(星期四)下午1:30-4:00

講題(一)：Asymptotic consistency of the maximum likelihood
　　　　　　　estimate in positron emission tomography.

主 講 人：張　憶　壽　　教授 (國立中央大學數學系)

摘 　　要

I will explain that the MLE of Vardi, Sheep and Kaufman can be regarded as a step in the standard nonparametric MLE by the method of sieves and will indicate the asymptotic consistency for it. This results suggests that the number of pixels needs to be in line with the number of detectors in　order to avoid poor image reconstructions. We will illustrate this by some simulation studies.

講題(二)：Some Statistical Analysis in PET (Positron Emission
　　　　　　　Tomography) and Ultrasound Images.

主 講 人：盧 鴻 興　　　教授 (國立交通大學統計科學研究所)

摘 　　要

(1) Due to the inherent ill-posedness of statistical inverse problems, the reconstructed images of positron emission tomography (PET) without regularization will have noise and edge artifacts. This is the limit of PET, which can not be resolved from the improvement of instrumental　designs. In order to have better reconstructed images, it is necessary to borrow the strength from the related information from expertise or other tomography systems, such as X-ray CT scan, MRI, and so forth. The correlated boundary information may offer the useful information in reducing the noise and edge artifacts. However, the boundary information may be incomplete or incorrect since the anatomy boundaries are different from the functional ones.Thus, cross-reference is important to make use the boundary information wisely. In this talk, we will present the cross-reference reconstruction methods for the weighted least square and maximum likelihood estimates. (2) Image segmentation is a fundamental and important step for image analysis. Tremendous efforts have been made to develop robust and efficient segmentation techniques in literature. However, segmentation for texture images remains as a challenging and unresolved problem due to its textural feature. While classical approaches may fail to give successful segmentation for texture images, human vision demonstrates its incredible ability in localizing the boundaries among various textures. Encouraged by the human visual performance, a new early vision model has been proposed in one of our previous works attempting to mimic the human visual perception. This talk will present new approaches for texture image segmentation and their applications in ultrasound images that are collected in the National Taiwan University Hospital.