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研究生: 馮偉哲
Fong, Wei-Jhe
論文名稱: 貝式推論在影像去模糊化上的應用
Blind Image Deconvolution via Bayesian Inference
指導教授: 吳金典
Wu, Chin-Tien
蔡志強
Tsai, Je-Chiang
口試委員: 張書銘
Chang, Shu-Ming
林得勝
Lin, Te-Sheng
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2022
畢業學年度: 110
語文別: 英文
論文頁數: 46
中文關鍵詞: 盲反迴旋捲積點擴散函數最大期望算法貝氏推論
外文關鍵詞: blind image deconvolution, Bayesian inference, Maximum a posteriori estimation, Expectation-maximization algorithm
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  • 在影像清晰的條件底下,我們能從其中獲得大量資訊。但時常由於硬體的設定或人為地因
    素,使得拍下照片變得模糊。由於無法清楚得知模糊的原因,因此在重建影像時需要同時估計模糊核。在只有一張模糊照片的情況下,同時重建影像及模糊核是個不適定性問題。雖然已經有許多演算法可以重建出相對清晰的影像,但這些方法裡時常忽略或是不清楚初始模糊核的估計。此篇論文探討利用 MAPk 的方法以廣義的狄拉克核為初始核來估計一個相對較接近真實的模糊核。我們會詳細推導其中的理論,並且應用於真實世界的影像上。


    Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown. This is an ill-posed problem since both true kernel with latent image and delta kernel with blur image can minimize the energy function. Therefore a good initial kernel that helps avoiding blur image with delta kernel for deblur process plays an essential role. Many research have already developed reasonable algorithms, but among them the initial blur kernel required for the algorithms are often unclear. This paper look into the MAPk algorithm based on Bayesian Inference, while the initial kernel of the process is always a delta kernel. The goal of this paper is to analyze and evaluate the blind image deconvolution method-MAPk both theoretically and experimentally. We derive the method mathematically and implement it on a real world images.

    Contents 摘要 i Abstract ii List of Figures iv 1 Background 1 1.1 Image Model 1 1.2 Probability Assumptions 3 2 Fitting the Image Prior 6 2.1 The Expectation-Maximization Algorithm 6 2.2 Why it works 9 3 MAPx,k and MAPk 11 3.1 Maximum A Posteriori estimation 11 3.2 MAPx,k 12 3.3 MAPk 14 3.3.1 Difference between MAPk and MAP via loss function perspective 15 3.3.2 EM based algorithm of MAPk 17 4 Non blind deconvolution 23 4.1 Fast TV-l1 Deconvolution 24 5 Numerical Results 27 6 Conclusions 44 References 45

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