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研究生:高瑞陽
論文名稱:應用壓縮取樣於具Apple core失真之斷層式數位全像顯微鏡系統
論文名稱(外文):On the Application of Compressed Sensing in Apple core Distortion of Tomographic Digital Holographic Microscope
指導教授:林立謙
口試委員:鄭超仁陳啟鏘
口試日期:2014-07-30
學位類別:碩士
校院名稱:逢甲大學
系所名稱:通訊工程學系
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:2014
畢業學年度:102
語文別:中文
論文頁數:40
中文關鍵詞:斷層式數位全像顯微術壓縮感知兩步迭代收縮閥值法
外文關鍵詞:Tomography digital holographic microscopyCompressive SeningTwo-Step Iterative Shrinkage/Thresholding
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斷層式數位全像顯微術(Tomography Digital Holographic Microscopy, TDHM)是一種能擷取物體三維資訊的技術,取得資訊的方法是固定物體並改變其照射角度,在本文照射光為紅色雷射光其波長接近於物體波長所以必須考慮繞射現象。
在本文使用傅立葉繞射投影定理(Fourier Diffraction Projection Theorem)來模擬斷層式數位全像顯微術(Tomography Digital Holographic Microscopy, TDHM)生成影像的過程,但因為斷層式數位全像顯微術(Tomography Digital Holographic Microscopy, TDHM)光學架構的入射角度限制因素使得重建物體在上下兩端會有較明顯的資訊遺失,而在頻率域上可以觀察到的現象則是一個類似於蘋果核的失真。
壓縮感知(Compressive Sening ,CS)技術的特性在於只要滿足必要條件稀疏性、測量矩陣與重建演算法就能從退化之影像重建出接近原始的影像,而本文會利用全變差展現實驗物體之稀疏性,使得影像退化的斷層式數位全像顯微術(Tomography Digital Holographic Microscopy, TDHM)光學架構作為測量矩陣,而重建演算法則為兩步迭代收縮閥值法。
Tomography Digital Holographic Microscopy provides a way to obtain fully three-dimeension imformation of the object based interference techniques. In this system, the coherence light source illuminates the rotating transparent micro-object and the transmitting wavefield is interfered with a reference plane wave. In digital holographic, one uses a charge-cover device (CCD) camera to record the hologram of the interference pattern and stored in the computer. For each rotating angle of the sample object, one can capture sectional information of the 3-D object. To integrate the holograms obtaining by the all rotating angles, one can reconstruct truly 3-D tomography information of the object.
We can use Fourier diffraction theory to simulate Tomography Digital Holographic Microscopy. Then, the sectional information of each rotating angle is sampling in the Fourier domain. The reconstruction algorithm then interpolates all data in the three-dimensional Fourier domain. The truly 3-D tomography information of the object can then be obtain by the 3-D inverse Fourier transform. However, by the diffraction theory, the data inside a region of the Fourier domain is loss by using the TDHM scanning technique, named as Apple core distortion, since the shape of the missing region looks like apple core. In this thesis, the compressive sensing algorithm is employed to accounts for the Apple-core distortion problem to achieve a better reconstruction.
Compressed sensing can be used as the image reconstruction for the inaccurate acquisition system. In this way, we have the sensing mechanism in the Fourier domain and the sparity of toatal variation. With this in mind, two-Step Iterative Shrinkage/Thresholding (TWIST) is developed for the reconstruction of the tomography data.
I. 緒論 1
1.1. 研究動機 1
1.2. 研究目的 1
1.3. 論文架構 2
II. 文獻探討 3
2.1.數位全像顯微術 3
2.1.1.數位全像顯微術系統架構 4
2.2.斷層式數位全像顯微術 5
2.2.1斷層式數位全像顯微術系架構 5
2.3.光學原理 7
2.3.1.傅立葉繞射投影定理 7
2.3.2.Cap之曲率 9
2.3.3.Direct Fourier Interpolation 10
2.4.壓縮感知(Compressive Sensing, CS) 13
2.4.1壓縮感知(Compressive Sensing, CS)之條件 13
2.4.2.重建演算法 16
2.4.3.兩步迭代收縮閥值法 17
2.4.4.維納濾波器 19
III. 數位模擬 20
3.1.Distortion Model 22
3.2. CS Reconstruction 28
IV. 結論與未來展望 38
V. 參考文獻 39
[1]A. T. Vouldis, C. N. Kechribaris, T. A. Maniatis, K. S. Nikita, and N. K. Uzunoglu, “Investigating the enhancement of threedimensional diffraction tomography by using multiple illumination planes,” J. Opt. Soc. Am. A., vol. 22, pp. 1251-1262, 2005.
[2]S. Vertu, J. J. Delaunay, O. Haeberle, “Diffraction microtomography with sample rotation influence of a missing apple core in the recorded frequency space”, Cent. Eur. J. Phys., vol. 7, pp. 22-31, 2009.
[3]S. X. Pan and A. C. Kak, “A Computational Study of Reconstruction Algorithms for Diffraction Tomography:Interpolation Versus Filtered Backpropagation”, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-31, pp. 1262-1275, 1983.
[4]J. M. Bioucas-Dias and M. A. T. Figueiredo, “A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration”, IEEE Transactions on Image Processing, 16(12), pp. 2992-3004, 2007.
[5]Emmanuel J. Candes and Michael B. Wakin, “An Introduction To Compressive Sampling”, IEEE Signal Processing Society, 25(2), pp.21-30, 2008.
[6]T. Zhang and I. Yamaguchi, “Three-dimensional microscopy with phase-shifting digital holography”, Opt. Lett, 23, pp.1221-1223, 1998.
[7]Jie Xu, Jianwei Ma, Dongming Zhang, Yongdong Zhang, and Shouxun Lin.Improved, “Improved total variation minimization method for compressive sensing by intra-prediction”, Signal Processing, 92(11), pp2614-2623, 2012.
[8]Jian Zhang, Shaohui Liu, Ruiqin Xiong, Siwei Ma, and Debin Zhao, “Improved Total Variation based Image Compressive Sensing Recovery by Nonlocal Regularization”, ISCAS, pp.2836-2839, 2013.
[9]C. Li, W. Yin, and Y. Zhang, “Users guide for tval3: TV minimization by augmented lagrangian and alternating direction algorithms”, CAAM report, 2009.
[10]José M. Bioucas-dias, Mário A. T. Figueiredo, “Two-step algorithms for linear inverse problems with non-quadratic regularization”, Image Processing, IEEE International Conference on Image Processing, pp.105-108, 2007.
[11]Michael Lustig, David Donoho, and John M. Pauly, “Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging”, Magnetic Resconance in Medicine, pp.1182-1195, 2007.
[12]邱聖耘,“斷層式數位全像顯衛系統之重建模型建構”, 逢甲大學通訊工程學系碩士論文, 2012.
[13]盧萱容,“Fresnel 全像片之壓縮技術研究”, 逢甲大學通訊工程學系碩士論文, 2013.
[14]謬紹綱,“數位影像處理-運用matlab”, 東華書局, 民94初版.
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