紅外線熱成像檢測(Infrared Thermography, IRT)屬於非破壞性檢測(Non-Destructive Testing, NDT)的一種檢測法，原理是藉由施加熱能於物體表面上，而各點的溫度變化會因為該點表面或內部材料影響熱傳效果，藉由熱像儀取得各像素點溫度值，且隨時間得到各點溫度變化情形，可進一步判斷是否有無缺陷隱藏在物體內部。而得到的溫度分布，會有不均勻的雜訊或是熱源不均的現象。此外，隨著時間的推移整個資料量是龐大的，但資料中存在著些許冗餘的數據，若未經處理得一一檢視各張圖片，耗時又費力，因此發展了許多分析法。而本研究藉由區域保留投影(Locality Preserving Projections, LPP)保留區域鄰近結構的概念，並將熱影像高維的數據投影至低維，達到降維的效果，且在低維空間中，還具有保持資料的局部結構，若有缺陷特性，則在低維空間中，LPPT應能保留此特性，並且顯示出來，此法稱為區域保留投影熱影像分析法(Locality Preserving Projections Thermography, LPPT)。另外，本研究應用稀疏主成分分析(Sparse Principal Component Analysis, SPCA)於熱影像分析，並採取軟閾值(soft-thresholding)解法，其優點是計算速度快且容易，調整單一參數即可，將此法稱作稀疏主成分熱影像分析法(Sparse Principal Component Thermography, SPCT)，SPCT是在原本的PCA問題中加入懲罰項L_1範數(L_1-norm)，達到稀疏的效果，改善主成分熱影像分析法(Principal component Thermography, PCT)主成分選取過多變數，噪聲(noise)影響過大，進而影響缺陷的判斷的缺點，且SPCT亦能達到壓縮數據的效果。除了LPPT和SPCT外，本研究應用獨立成分分析法(Independent Component Analysis, ICA)演算法中最大化非高斯性、進行盲源分離的概念，提出獨立成分熱影像分析法(Independent Component Thermography, ICT)，試圖將熱影像分離出背景的訊號以及缺陷的部分，以達到缺陷檢測的目的，做法是以每張圖片做為觀測信號，分離出獨立成分(independent component, IC)，並藉由峰度(kurtosis)作為輔助判斷，判斷獨立成分的非高斯性，峰度高即有著極端值的影響，即有一定的機率檢測出缺陷存在。

Infrared Thermography (IRT) is a popular method for Non-Destructive Testing (NDT). The principle of IRT is as follows. By applying thermal energy to the surface of the object under investigation, the surface temperature will change along time and show certain patterns that associate with the internal material properties. By recording the temperature values at each pixel with an infrared thermal camera, it can be judged whether there is a defect inside the object or not. However, the thermal images are usually disturbed by significant non-uniform backgrounds and noise. In addition, the thermal data are often numerous and contain redundant information. Therefore, thermal data analytics become a necessity.
In this study, the concept of Locality Preserving Projections (LPP) was applied to IRT. This linear tramsformation preserves local neighborhood information of the original data and at the same time ahieves dimensionality reduction. Its applicaiton to the thermographic data analysis field was named Locality Preserving Projections Thermography (LPPT). Next, a Sparse Principal Component Thermography (SPCT) method was proposed, which was enlighted by Sparse Principal Component Analysis (SPCA). Experiment results show that SPCT outperforms Principal Component Thermography (PCT) because it leads to more sparse loading images which are easier to be interpreted. At last, Independent Component Thermography (ICT) was also proposed in this work, which applies Independent Component Analysis (ICA) for detect detection based on thermal images. Based on the concept of blind source separation, ICT tries to separate the signals corresponding to normal and defective regions. The kurtosis statistic is used as an index to measure the non-Gaussionity of the signals. The Independent Components (ICs) with higher kurtosis values have larger chances to contain extreme values. In other words, they have higher probabilties to detect the existence of defects.

一、緒論..........................................................1
1.1前言..........................................................1
1.2文獻回顧和研究動機..............................................2
1.3文章架構.......................................................4
二、研究方法......................................................5
2.1熱影像數據處理流程..............................................5
2.2 LPP/LPPT.....................................................7
2.2.1區域保留投影Locality Preserving Projections, LPP.............7
2.2.2區域保留投影熱影像分析法 Locality Preserving Projections Thermography, LPPT...............................................8
2.3 SPCA/SPCT....................................................9
2.3.1稀疏主成分分析法Sparse Principal Component analysis, SPCA.....9
2.3.2稀疏主成分熱影像分析法 Sparse Principal Component Thermography, SPCT............................................................12
2.4 ICA/ICT.....................................................14
2.4.1獨立成分分析法Independent Component Analysis, ICA............14
2.4.2獨立成分熱影像法Independent Component Thermography, ICT......17
三、結果與討論....................................................18
3.1樣本與實驗數據介紹.............................................18
3.1.1碳纖維補強高分子(Carbon Fiber Reinforced Polymer, CFRP-1)....18
3.1.2 CFRP-2....................................................19
3.1.3木頭鑲嵌樣本................................................20
3.1.4古鑲嵌物...................................................22
3.1.5 Madonna油畫................................................24
3.1.6義大利古壁畫................................................26
3.2 CFRP-1研究成果...............................................27
3.2.1 CFRP-1 LPPT結果............................................29
3.2.2 CFRP-1 PCT結果.............................................30
3.2.3 CFRP-1 SPCT結果............................................31
3.2.4 CFRP-1 SPCT不同λ 值之比較..................................32
3.2.5 CFRP-1 ICT結果.............................................33
3.2.6 CFRP-1 結果討論............................................35
3.3 CFRP-2 研究成果..............................................36
3.3.1 CFRP-2 LPPT結果............................................38
3.3.2 CFRP-2 PCT結果.............................................40
3.3.3 CFRP-2 SPCT結果............................................41
3.3.4 CFRP-2 SPCT不同λ 值之比較..................................42
3.3.5 CFRP-2 ICT結果.............................................43
3.3.6 CFRP-2 結果討論...........................................45
3.4木頭鑲嵌樣本 研究成果..........................................46
3.4.1木頭鑲嵌樣本 LPPT結果........................................48
3.4.2木頭鑲嵌樣本 PCT結果........................................49
3.4.3木頭鑲嵌樣本 SPCT結果........................................50
3.4.4木頭鑲嵌樣本SPCT不同λ 值之比較................................51
3.4.5木頭鑲嵌樣本 ICT結果.........................................52
3.4.6木頭鑲嵌樣本 結果討論........................................54
3.5古鑲嵌物 研究成果..............................................55
3.5.1古鑲嵌物 LPPT結果...........................................57
3.5.2古鑲嵌物 PCT結果...........................................58
3.5.3古鑲嵌物 SPCT結果...........................................59
3.5.4古鑲嵌物SPCT不同λ 值之比較..................................60
3.5.5古鑲嵌物ICT結果............................................61
3.5.6古鑲嵌物 結果討論...........................................63
3.6 Madonna油畫 研究成果.........................................64
3.6.1 Madonna油畫 LPPT結果.......................................66
3.6.2 Madonna油畫 PCT結果........................................67
3.6.3 Madonna油畫 SPCT結果.......................................68
3.6.4 Madonna油畫 SPCT不同λ 值之比較..............................69
3.6.5 Madonna油畫 ICT結果........................................70
3.6.6 Madonna油畫 結果討論.......................................72
3.7義大利古壁畫 研究成果..........................................73
3.7.1義大利古壁畫 LPPT結果........................................75
3.7.2義大利古壁畫 PCT結果.........................................76
3.7.3義大利古壁畫 SPCT結果........................................77
3.7.4義大利古壁畫SPCT不同λ 值之比較................................78
3.7.5義大利古壁畫 ICT結果.........................................79
3.7.6 義大利古壁畫 結果討論.......................................81
四、結論.........................................................82
五、參考文獻.....................................................84

Drapier, S., et al., Characterization of transient through-thickness permeabilities of non crimp new concept (NC2) multiaxial fabrics. Composites Part A: Applied Science and Manufacturing, 2005. 36(7): p. 877-892.
2. Stefanesco, S., C. Schlumberger, and M. Schlumberger, Sur la distribution électrique potentielle autour d'une prise de terre ponctuelle dans un terrain à couches horizontales, homogènes et isotropes. Journal de Physique et le Radium, 1930. 1(4): p. 132-140.
3. Burke, S., S.M. Cousland, and C. Scala. Nondestructive characterization of advanced composite materials. in Materials Forum. 1994. 18: p.85-109
4. Vavilov, V., et al., Thermal nondestructive testing of carbon epoxy composites: detailed analysis and data processing. NDT & E International, 1993. 26(2): p. 85-95.
5. Almond, D.P., et al. Round Robin comparison II of the capabilities of various thermographic techniques in the detection of defects in carbon fibre composites. in Quantitative Infrared Thermography (QIRT2000) Eurotherm Seminar 64. 2000. University of Bath.
6. Liu, J., et al. Research on CFRP materials nondestructive testing by IR lock-in thermography. in International Symposium on Photoelectronic Detection and Imaging 2009: Advances in Infrared Imaging and Applications. 2009. International Society for Optics and Photonics. Beijing, China.
7. BuSSe, G., D. Wu, and W. Karpen, Thermal wave imaging with phase sensitive modulated thermography. Journal of Applied Physics, 1992. 71(8): p. 3962-3965.
8. Pickering, S. and D. Almond, Matched excitation energy comparison of the pulse and lock-in thermography NDE techniques. Ndt & E International, 2008. 41(7): p. 501-509.
9. Maldague, X. and S. Marinetti, Pulse phase infrared thermography. Journal of applied physics, 1996. 79(5): p. 2694-2698.
10. Pilla, M., et al. New absolute contrast for pulsed thermography. in Proc. QIRT. 2002. Dubrovnik, Croatia.
11. Rajic, N., Principal component thermography. 2002, defence science and technology organisation Victoria(Australia) aeronautical and maritime research lab.
12. Shepard, S.M., System for generating thermographic images using thermographic signal reconstruction. 2004, Google Patents.
13. Maierhofer, C., et al., Characterizing damage in CFRP structures using flash thermography in reflection and transmission configurations. Composites Part B: Engineering, 2014. 57: p. 35-46.
14. He, X. and P. Niyogi. Locality preserving projections. in Advances in neural information processing systems. 2004. 16: p.153-160
15. Yu, W., X. Teng, and C. Liu, Face recognition using discriminant locality preserving projections. Image and Vision computing, 2006. 24(3): p. 239-248.
16. Zou, H., T. Hastie, and R. Tibshirani, Sparse principal component analysis. Journal of computational and graphical statistics, 2006. 15(2): p. 265-286.
17. Sjöstrand, K., et al., Spasm: A matlab toolbox for sparse statistical modeling. Journal of Statistical Software Accepted for publication, 2012.
18. Madruga, F.J., et al., Infrared thermography processing based on higher-order statistics. NDT & E International, 2010. 43(8): p. 661-666.
19. Hyvarinen, A., Fast and robust fixed-point algorithms for independent component analysis. IEEE transactions on Neural Networks, 1999. 10(3): p. 626-634.
20. Bingham, E. and A. Hyvärinen, A fast fixed-point algorithm for independent component analysis of complex valued signals. International journal of neural systems, 2000. 10(01): p. 1-8.
21. 郭學哲, 適應性核獨立成份分析 (KICA) 於非線性流程之監控. 朝陽科技大學工業工程與管理系碩士在職專班學位論文, 2011: p. 1-79.
22. Vines, S., Simple principal components. Journal of the Royal Statistical Society: Series C (Applied Statistics), 2000. 49(4): p. 441-451.
23. Cadima, J. and I.T. Jolliffe, Loading and correlations in the interpretation of principle compenents. Journal of Applied Statistics, 1995. 22(2): p. 203-214.
24. Comon, P., Independent component analysis, a new concept? Signal processing, 1994. 36(3): p. 287-314.
25. Bell, A.J. and T.J. Sejnowski. A non-linear information maximisation algorithm that performs blind separation. in Advances in neural information processing systems. 1995. p.467-474. The MIT Press, Cambridge, MA.
26. Bell, A.J. and T.J. Sejnowski, An information-maximization approach to blind separation and blind deconvolution. Neural computation, 1995. 7(6): p. 1129-1159.
27. Hyvärinen, A. New approximations of differential entropy for independent component analysis and projection pursuit. in Advances in neural information processing systems 10. 1998. p.273-279. MIT Press.
28. 連憶如，胡竹生，頻域獨立成分分析法於語音訊號分離之研究，國立交通大學電機與控制工程研究所碩士論文，2003。
29. 張嘉芳，胡竹生，以 FastICA 為基礎之時域聲音分離演算法，國立交通大學電機與控制工程研究所碩士論文，2002。
30. Sfarra, S., et al., Inspecting marquetries at different wavelengths: the preliminary numerical approach as aid for a wide-range of non-destructive tests. Journal of Nondestructive Evaluation, 2017. 36(1): p. 6.