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研究生:李佩璇
研究生(外文):Pei-Shuan Lee
論文名稱:應用傅立葉小波轉換於正子斷層掃描正弦圖去雜訊及影像重建
論文名稱(外文):Simultaneous denoising and reconstruction of PET sinogram using Fourier-Wavelet transform
指導教授:陳祺賢林康平林康平引用關係
指導教授(外文):Chi-Hsien ChenKang-Ping Lin
學位類別:碩士
校院名稱:中原大學
系所名稱:電機工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:54
中文關鍵詞:正子斷層掃描小波去雜訊傅立葉小波正規反迴旋積分濾波反投影
外文關鍵詞:filtered back projectionFourier- Wavelet regularized deconvolutionwavelet denoise projectionpositron emission tomography
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正子斷層造影是利用偵測正子與電子互毀產生之光子對,將偵檢器偵測到的偶合事件儲存於正弦圖中,再經由影像重建方法還原成切面影像。在造影過程中正子斷層掃描影像因光子的散射、衰減等物理性質或系統的偵測效率等問題,使偵檢系統誤判放射源之投影角度與投影位置,造成正弦圖中有部份錯誤的資料,使得重建後的影像品質劣於其他醫學影像。
  本研究目的為降低正弦圖中的錯誤資訊,根據傅立葉小波正規反迴旋積分理論,同時利用頻域與時頻域去雜訊的優點將雜訊濾除。訊號經由傅立葉轉換至頻域後,雜訊明顯的分佈於高頻區域,因此可以利用濾波器將部份雜訊濾除,但是若高頻訊號濾除過多,容易造成訊號失真。而小波轉換去雜訊具有時頻定位及多重解析的優點,訊號經小波轉換多層分解至時頻域後,尺度係數為訊號之近似部份,小波係數為訊號之高頻細節部份,藉由濾除小波係數,最後可得到去除雜訊之訊號並可保留訊號特徵部份。本文利用頻域濾波器去雜訊與小波去雜訊方法於正弦圖上,使用濾波反投影法重建影像,以提升其重建影像之影像品質。
Positron Emission Tomography(PET) detect the coincidence by detecting gamma rays produced by positron and electron’s annihilation, and ten save the coincidence event in sinogram. After that, we can reconstruction the slice image by sinogram. The PET system will have erroneous judgement on radioactive source’s projection angle and projection position, because of the gamma ray’s detecting efficiency of system or physical properties such as scatter and attenuation. It will cause some wrong information in sinogram and make the image’s quality not as good as other medical image, such as CT and MRI.

In our study, we will based on the Fourier-Wavelet Regularized Deconvolution (ForWaRD) and the advantage by using time-frequency domain to reduce the wrong information in sinogram and filter out noise. After signal transfer to frequency by using Fourier transform, noise always spread at the high frequency area, we can use filter to filter out noise. On the other hand, if we filter out much signal at high frequency area, it will make signal distortion. Otherwise, denoise using wavelet transform will have advantages such as time-frequency location and multi-resolution after signal transfer in time-frequency domain, the scaling coefficient is similar to signal, and wavelet coefficient is the detail of the high frequency part. By filtering out wavelet coefficient, we can get the signal without noise and keep the characteristic of signal. In order to promote the quality of reconstruction image, in this thesis, we use Fourier and wavelet denoise in sinogram, and then use filtered back projection to reconstruct the PET image.
目 錄
中文摘要.........................................................I
Abstract........................................................II
致謝...........................................................III
目錄............................................................IV
圖表目錄........................................................VI

第一章 緒論....................................................1
1.1 研究背景 ...............................................1
1.2 研究動機與目的 .........................................2
1.3 論文架構 ...............................................4

第二章 正子斷層掃描基本原理....................................5
2.1 正子斷層掃描造影原理 ...................................5
2.2 正子斷層掃描影像影響因素 ...............................6
2.2.1 散射偶合 ...............................................7
2.2.2 隨機偶合 ...............................................8
2.3 資料儲存-正弦圖 ......................................9
2.4 濾波反投影影像重建 ....................................12

第三章 傅立葉小波轉換去雜訊法.................................16
3.1 含雜訊之訊號系統 .....................................16
3.2 轉換域去雜訊理論 ......................................17
3.3 小波轉換去雜訊理論 ....................................19
3.3.1 小波轉換理論 ..........................................20
3.3.2 時頻域去雜訊 ..........................................28

第四章 應用去雜訊方法於正弦圖.................................32
4.1 小波轉換去雜訊於正弦圖 ................................34
4.2 傅立葉轉換去雜訊於正弦圖...............................36

第五章 實驗結果與討論.........................................38
5.1 小波轉換去雜訊實驗結果.................................38
5.2 傅立葉小波轉換去雜訊實驗結果...........................42
5.2.1 四等份圓柱假體實驗結果 ................................42
5.2.2 小鼠造影實驗結果.......................................46

第六章 結論與未來展望.........................................50
Reference.......................................................51
作者簡歷........................................................54


圖表目錄
圖2-1 正子放射與電子互毀............................................5
圖2-2 PET環型偵檢器偵測偶合事件.....................................6
圖2-3 PET偶合事件種類...............................................7
圖2-4 PET造影流程圖................................................10
圖2-5 PET系統(a)LOR於transaxial平面; (b)正弦圖.....................10
圖2-6投影角度 之 (a)受測體的投影平面; (b)受測體之正弦圖............11
圖2-7 Radon轉換,角度θ=135°時投影平面上 之線積分值.................13
圖2-8濾波反投影之Ramp、Hanning濾波器於頻域中分布情形...............15
圖3-1原始訊號x經過線性非時變系統後加入高斯雜訊之結果...............16
圖3-2 ForWaRD去雜訊流程圖..........................................17
圖3-3尺度函數與小波函數空間........................................23
圖3-4二階尺度小波轉換分析示意圖....................................25
圖3-5二階尺度小波轉換合成示意圖....................................25
圖3-6二維小波轉換分析、合成示意圖..................................27
圖3-7二階尺度二維影像小波分析架構圖................................28
圖3-8時域、頻域、時頻域之比較......................................29
圖3-9時頻域去雜訊流程圖............................................29
圖3-10 thresholding 示意圖..........................................30
圖4-1原始影像、正弦圖、投影計數量分佈圖............................32
圖4-2正弦圖以傅立葉小波轉換去雜訊流程圖 ...........................33
圖4-3正弦圖傅立葉小波轉換去雜訊流程圖..............................33
圖4-4小波分解以方波訊號為例........................................34
圖4-5小波轉換去雜訊之小波係數與結果................................36
圖4-6傅立葉小波轉換去雜訊訊號示意圖................................37
圖5-1四等份圓柱假體之正弦圖、FBP重建影像...........................43
圖5-2四等份圓柱假體ROI.............................................45
圖5-3四小鼠正子斷層造影之正弦圖、FBP、前肢ROI、胸腔切面ROI.........46

表3-1小波轉換濾波係數..............................................39
表5-1原始方波訊號..................................................39
表5-2雜訊std = 10%取不同臨界值之去雜訊效果.........................39
表5-3雜訊std = 15%取不同臨界值之去雜訊效果.........................40
表5-4訊號雜訊std = 10%取不同臨界值之SNR值比較......................41
表5-5雜訊std = 15%取不同臨界值之SNR值比較..........................41
表5-6雜訊std = 10%與 15 % 取不同臨界值之SNR值圖表..................41
表5-7四等份圓柱假體之正弦圖 之曲線分佈.............................43
表5-8 四等份圓柱假體取不同臨界值去雜訊之重建影像效果四等份圓柱假體取
體取不同臨界值去雜訊之重建影像效果...........................44
表5-9四等份圓柱假體去雜訊之重建影像灰階值分布ROI標準差比較.........45
表5-10四等份圓柱假體去雜訊之重建影像ROI標準差比較..................45
表5-11小鼠造影取不同臨界值去雜訊之重建影像效果與第155列之灰階值分佈
圖..........................................................47
表5-12小鼠造影去雜訊之重建影像灰階值分布ROI標準差比較..............48
表5-13小鼠正子斷層造影去雜訊之重建影像ROI標準差比較................48
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