博碩士論文 110225018 完整後設資料紀錄

DC 欄位 語言
DC.contributor統計研究所zh_TW
DC.creator許毓玹zh_TW
DC.creatorYU-HSUAN HSUen_US
dc.date.accessioned2023-7-24T07:39:07Z
dc.date.available2023-7-24T07:39:07Z
dc.date.issued2023
dc.identifier.urihttp://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=110225018
dc.contributor.department統計研究所zh_TW
DC.description國立中央大學zh_TW
DC.descriptionNational Central Universityen_US
dc.description.abstract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。zh_TW
dc.description.abstractIn 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.en_US
DC.subject赤池信息量準則zh_TW
DC.subject固定秩克里金zh_TW
DC.subject廣義自由度zh_TW
DC.subject高維度反矩陣zh_TW
DC.subject醫學影像zh_TW
DC.subjectAkaike′s information criterionen_US
DC.subjectfixed rank krigingen_US
DC.subjectgeneralized degrees of freedomen_US
DC.subjecthigh-dimensional inverse matrixen_US
DC.subjectmedical imageen_US
DC.title固定秩克里金法的圖像重建zh_TW
dc.language.isozh-TWzh-TW
DC.titleImage reconstruction based on fixed rank krigingen_US
DC.type博碩士論文zh_TW
DC.typethesisen_US
DC.publisherNational Central Universityen_US

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