多通道盲蔽影像反捲積(multichannel blind image deconvolution, MBID)的問題是在沒有任何有關真實(原始)影像(true or original image)與模糊函數(blur function)的訊息下(除了一些基本的假設之外)，如何從多張模糊影像(blurred image)中還原真實影像。在這篇論文中，我們用滑動的視窗將所有的模糊影像做資料重組，重新公式化多通道盲蔽影像反捲積的問題為一個多輸入多輸出(multi-input multi-output, MIMO)的問題，其中多個輸入是利用視窗所獲取真實影像中不同的子影像(sub-image)。然後利用凸分析與多個子影像間彼此的關係，我們提出一個基於凸分析之多通道盲蔽影像反捲積(a convex analysis based MBID, CAMBID)準則，及發展出其演算法，同時藉由最小平方解來實現這個準則。在雜訊不存在的情況下，我們證明基於凸分析之多通道盲蔽影像反捲積演算法對真實影像的鑑別能力。模擬資料顯示相對於其它現存的演算法，我們所提出的演算法在較高的訊雜比下有較好的性能，同時也需要較少的運算時間(computation time)。

The multichannel blind image deconvolution (MBID) problem is how to recover a single true (original) image from multiple blurred images without resorting to any prior knowledge about the true image and the blur functions (except for some general assumptions). In this thesis, we employ a sliding window which shifts over the whole blurred images for data rearrangement to formulate the MBID problem as a multi-input multi-output (MIMO) problem, where the multiple inputs correspond to different sub-images of the true image. By convex analysis and the relationship among these sub-images, we propose a convex analysis based MBID (CAMBID) criterion, and develop an algorithm that fulfills the criterion by the least squares solution. We show the true image identifiability of the CAMBID criterion in the absence of noise. Some simulation results are presented to demonstrate that our proposed algorithm provides better performance for higher SNRs and less computation time than several existing benchmark algorithms.

摘要 i
Abstract ii
誌謝 iii
目錄 iv
第一章 緒論 1
1.1 簡介 1
1.2 論文架構 2
第二章 問題描述與重建訊號模型 3
第三章 訊號模型假設與凸分析的基本觀念 6
3.1 訊號模型假設 6
3.2 仿射包(Affine Hull) 7
第四章 提出多通道盲蔽影像反捲積演算法 9
4.1 基於凸分析之多通道盲蔽影像反捲積演算法準則(CAMBID Criterion) 10
4.2 基於凸分析之多通道盲蔽影像反捲積演算法(CAMBID) 11
第五章 電腦模擬 15
5.1 模擬參數定義與設定 15
5.2 模擬結果與分析 16
第六章 結論 26
第七章 參考文獻 27
第八章 附錄 29
A. Theorem 1之證明 29

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