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研究生:許濬濠
研究生(外文):Syu, Jyun-Hao
論文名稱:一個混合型迭代算法在影像去模糊問題的研究
論文名稱(外文):The Study on Image Deblurring Problems by a Hybrid Algorithm from Optimization Problem
指導教授:莊智升
指導教授(外文):Chuang, Chih-Sheng
口試委員:莊智升陳嘉文洪宗乾
口試委員(外文):Chuang, Chih-ShengChen, Jia-WenHong, Chung-Chien
口試日期:2022-07-07
學位類別:碩士
校院名稱:國立嘉義大學
系所名稱:應用數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2022
畢業學年度:110
語文別:中文
論文頁數:67
中文關鍵詞:圖像去模糊點擴散函數卷積凸優化問題正則化
外文關鍵詞:Image DeblurringPoint Spread FunctionConvolutionConvex OptimizationRegularization
相關次數:
  • 被引用被引用:0
  • 點閱點閱:77
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  • 下載下載:12
  • 收藏至我的研究室書目清單書目收藏:0
在目前的科技世代,獲取相片與影片的技術門檻大幅降低,不再侷限於昂貴的攝影設備。當人們看到一個想紀錄留念的場景時,只需要拿出手機即可記錄下來。然而快速的同時,也代表著不夠專業,可能是鏡頭品質不好,抑或是自身未受過攝影相關訓練等,往往導致成像是模糊的,因此本研究希望從演算法的角度,將模糊圖像去模糊,進而獲得清晰的圖像。
圖像去模糊是從模糊的圖像 B 中恢復一個清晰的圖像 X,其中 X 與 A(模糊矩陣)卷積以生成 B。從數學模型而言,這可以表示為 B=A*X (其中 * 表示卷積)。在此,我們從最佳化理論的角度出發,考慮一個抽象的最佳化問題,並進而提出一個新的混合型迭代算法,及其收斂理論,並以此應用在影像去模糊的問題上。最後,我們呈現數值結果來說明這個算法的優點。
In this technological era where everyone has a smartphone, the threshold for obtaining photos and videos has been greatly lowered, and it is no longer limited to expensive photographic equipment. When people see a scene they want to record as a souvenir, they just need to take out their smartphone to record it. However, at the same time, it also means that it is not professional enough. It may be that the quality of the lens is not good, or that you have not received photography-related training, etc., often results in blurry images. Therefore, this research hopes to deblur the blurred image from the perspective of algorithm.
Image deblurring recovers a sharp image X from a blurred image B, where X is convolved with A (a blur matrix) to produce B. Mathematically, this can be expressed as B=A*X (where * means convolution). Here, we consider an abstract optimization problem, and propose a new hybrid iterative algorithm with related convergence theory, and apply it to the image deblurring problem. Finally, we present numerical results to illustrate the advantages of this algorithm.
摘要 I
Abstract II
目錄 III
1 圖像去模糊問題 1
1.1 前言與研究動機 1
1.2 圖像如何變成數位陣列 2
1.3 模糊圖像與簡單的線性模型 6
1.4 去模糊地第一次嘗試 8
1.5 廣義線性模型 9
2 在Python 中處理圖像 15
2.1 Python 環境 15
2.1.1 Python 的設定 15
2.1.2 Anaconda 的設定 16
2.1.3 OpenCV 的設定 16
2.2 圖像基礎 17
2.3 讀取、顯示和儲存圖像 17
2.4 對圖像進行算術運算 19
2.5 重新審視顯示和儲存 21
3 模糊函數 22
3.1 前言 22
3.2 數學模型中的矩陣 23
3.3 獲取點擴散函數(PSF) 25
3.4 雜訊 29
3.5 邊界條件 30
4 結構化矩陣計算 35
4.1 基本結構 36
4.1.1 一維問題 36
4.1.2 二維問題 40
5 混合型迭代演算法 42
5.1 背景 42
5.2 先備知識 46
5.3 混合型迭代演算法(H I A) 50
5.4 數值結果 55
5.5 總結 63
參考文獻 64
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李立宗編著,(2020) 科班出身的AI人必修課:OpenCV影像處理使用 Python,深智數位股份有限公司。

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