臺灣博碩士論文加值系統

影像經常會因為各種原因受到雜訊的干擾，所以去雜訊對於影像處理的應用是一種很重要的技術。非區域均值演算法(Non-Local Means，以下稱為NLM)的去雜訊是透過比較區塊的方式去實現，它會比較某一特定位置的區塊並與其他鄰近的區塊做相似度的權重計算，接下來將所有鄰近像素的權重平均取代原本的像素值。NLM是利用相似區塊的概念進行去雜訊，後面發展出的三維區塊匹配演算法(Block-Matching 3D，以下稱為BM3D)也是藉由利用區塊匹配尋找相似區塊的概念進行去雜訊。BM3D演算法是將影像相似的2D區塊堆疊成一個3D的矩陣，稱為群，透過對群進行協同濾波的去雜訊方式來完成。協同濾波程序有三個步驟:(1)3D轉換，(2)轉換後頻譜係數的縮減，(3)3D逆轉換。BM3D是透過兩個階段去雜訊來實現，兩個階段都是先利用區塊匹配找出相似的區塊，在使用協同濾波進行去雜訊，其中第一階段的協同濾波是使用Hard Thresholding進行頻譜係數的縮減，第二階段則是使用Wiener Filtering進行頻譜係數的縮減。根據上述，在這邊能夠得到三種不同方式的去雜訊演算法: NLM去雜訊演算法、三維區塊匹配第一階段演算法與三維區塊匹配第二階段演算法。
本論文的研究方向是通過將NLM及BM3D兩個階段的去雜訊演算法進行兩個階段的組合，嘗試在一共九種搭配中找出一個最好的組合。由於BM3D第二階段去雜訊演算法作為第一階段的去雜訊效果很差，所以本論文並不會對此組合進行討論，因此撇除這個方法後，一共會有六種不同的組合。實驗結果顯示，將NLM作為第一階段以及BM3D第一階段去雜訊演算法作為第二階段的組合有最佳的表現，在去雜訊影像品質微幅下降的情況下，提升了原本BM3D的執行速度2.98倍。

Since digital images are often interfered by noises from various sources, image denoising is an important technique in image processing. Non-local means (NLM) algorithm achieves denoising through block matching. It compares the block of a pixel to be denoised with its neighboring blocks and uses the weighted average of all the neighboring pixels to remove noises. Later, block-matching 3D (BM3D) algorithm also uses the concept of block matching in image denoising. BM3D gathers similar blocks into a 3D group. It then uses collaborative filtering in these 3-D groups to remove noises. Collaborative filtering is accomplished in three steps: 1) 3D transformation of a group, 2) shrinkage of the transform coefficients, and 3) inverse 3D transformation. BM3D repeats the above block matching and collaborative filtering approach twice. In the first stage, hard thresholding is used in the shrinkage of the transform coefficients. In the second stage, Wiener filtering is used in the shrinkage. Therefore, there are three different denoising blocks from NLM and BM3D: a NLM denoising block, a BM3D denoising block in its first stage, and a BM3D denoising block in its second stage.
By combining these three blocks in two steps, this thesis aims to find the best combination among the nine possibilities. Since the second stage of the BM3D require a reference with small noise interference, it cannot achieve acceptable denoising performance if put at the first step of the combination. Therefore, this thesis considers the other six combination by eliminating the second stage of BM3D from the first step of the combination. Experimental results demonstrate that NLM in the first step combined with the first stage of BM3D in the second step can speed up the processing by 2.98 times with only a small sacrifice in denoising performance.

誌謝 i
摘要 ii
Abstract iii
目次 iv
表目次 v
圖目次 vi
第一章　緒論 1
1.1簡介 1
1.2論文架構 2
第二章　背景介紹 3
2.1 非區域均值演算法(Non-Local Means) 3
2.2 BM3D演算法介紹 6
2.3 第一階段去雜訊 6
2.4 第二階段去雜訊 9
2.5 總結 11
第三章　研究方法 12
3.1 非區域均值演算法結合三維區塊匹配去雜訊演算法 12
3.2 以BM3Ds1為第一階段結合三種不同去雜訊演算法 14
3.3 以NLM為第一階段結合三種不同去雜訊演算法 16
3.4 總結 19
第四章　實驗結果與分析 20
4.1 實驗環境、設備與參數設定之介紹 20
4.2 BM3D結合NLM實驗結果 23
4.2.1 NLM-NLM實驗結果 25
4.2.2 BM3Ds1-NLM實驗結果 29
4.2.3 NLM-BM3Ds2實驗結果 33
4.2.4 NLM-BM3Ds1實驗結果 37
4.3實驗結果與比較 41
4.4 總結 48
第五章　結論 49
參考文獻 50

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