在影像研究中，影像的底層結構通常呈現出空間非平穩特徵。適當地指定空間相關性的非平穩函數以重建影像是一個具有挑戰性的問題。此外，重建高解析度影像的計算問題也是另一項挑戰，因為這可能耗時甚至無法執行。在本篇論文中，我們運用薄板樣條（Thin-plate spline）技術在空間迴歸模型中對影像的空間相關性進行建模。我們提出均方預測誤差（MSPE）準則，評估並選取一個適當的抽樣方法和適中的樣本數，為了充分降維並重建感興趣的影像。我們透過各種模擬情境來評估所提出的MSPE準則的有效性，並以氣象和醫學影像的兩個實際數據說明方法的實用性。;In image studies, the underlying structure of images generally shows spatially nonstationary features. Appropriately specifying a nonstationary covariance function for the inherent spatial correlation to reconstruct the underlying image of interest is a challenging problem. In addition, the computational issue about reconstructing high-resolution images is also another challenge, as it can be time-consuming or even infeasible. In this thesis, we apply the thin-plate spline technique to model the underlying spatial correlation of images within spatial regression models. To achieve dimension reduction, we then propose a mean squared prediction error (MSPE) criterion to determine an appropriate sampling method with a moderate sample size to reconstruct the underlying image of interest. We assess the empirical performance of the proposed MSPE criterion via various simulation scenarios and two real data examples regarding meteorology and medical imaging are presented for illustration.
