固定秩克里金法的圖像重建

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許毓玹(YU-HSUAN HSU) 查詢紙本館藏

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論文名稱

固定秩克里金法的圖像重建
(Image reconstruction based on fixed rank kriging)

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至系統瀏覽論文 (2026-7-1以後開放)

摘要(中)

在醫學圖像研究中，圖像的主體內部通常呈現非平穩的空間特徵。而如何為此空間相關過程適當地指定一個非平穩相關函數來重建內部截面的圖像是一個棘手的問題。在本文中，我們使用非參數的特徵函數來刻畫潛在的空間相關隨機過程。然後，我們從預測的觀點提出均方預測誤差 (MSPE) 準則來確定特徵函數的數量。我們所提出的想法不需要指定特定的空間相關結構，並且能應用於大量數據集且避免處理高維度反矩陣議題。因此，它比傳統方法更具實用性。我們將藉由數值實驗探討 MSPE 準則的表現，並且，分析降雨數據和大腦的磁振造影（MRI）圖像驗證方法的適用時機。

摘要(英)

In medical image studies, the image of a subject′s internal section generally shows spatially nonstationary feature. How to appropriately specify a nonstationary covariance function for inherent spatial correlation processes to reconstruct the underlying image of the internal section is an intractable problem. In this thesis, we use a nonparametric technique based on an eigen decomposition to model the underlying spatial covariance processes. We then propose a mean square prediction error (MSPE) criterion based on the generalized degrees of freedom to determine the number of eigenfunctions. The proposed idea is not required to set a specific covariance structure and can be applied to massive data sets without handling high-dimensional inverse matrices. As a result, it is more flexible than the conventional methods. The effectiveness of the proposed MSPE criterion is evaluated via various numerical experiments. Finally, a rainfall real data and a MRI image of brain are analyzed for illustration.

關鍵字(中)

★ 赤池信息量準則
★ 固定秩克里金
★ 廣義自由度
★ 高維度反矩陣
★ 醫學影像

關鍵字(英)

★ Akaike′s information criterion
★ fixed rank kriging
★ generalized degrees of freedom
★ high-dimensional inverse matrix
★ medical image

論文目次

1 Introduction 1
2 A flexible spatial regression model 3
2.1 Spatial regression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Modeling spatial covariance structure . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Spatial prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3 Determination the number of eigenfunctions 8
3.1 Akaike’s information criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Mean square prediction error . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4 Simulation 12
4.1 Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 Application 23
6 Conclusion and discussion 32
Reference 33

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指導教授

陳春樹(Chun-Shu Chen)

審核日期

2023-7-24

推文