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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 林致廷 | zh_TW |
dc.contributor.advisor | Chih-Ting Lin | en |
dc.contributor.author | 陳逵禎 | zh_TW |
dc.contributor.author | Chen-Kuei Chen | en |
dc.date.accessioned | 2024-03-04T16:22:59Z | - |
dc.date.available | 2024-03-05 | - |
dc.date.copyright | 2024-03-04 | - |
dc.date.issued | 2024 | - |
dc.date.submitted | 2024-02-16 | - |
dc.identifier.citation | [1] Nyquist, Harry. "Certain topics in telegraph transmission theory." (1928): 617-644.
[2] Shannon, Claude Elwood. "Communication in the presence of noise." Proceedings of the IRE 37.1 (1949): 10-21. [3] Pope, Graeme. ”Compressive sensing: A summary of reconstruction algorithms.” Diss. ETH, Swiss Federal Institute of Technology Zurich, Department of Computer Science, 2009. [4] S. Qaisar, R. M. Bilal, W. Iqbal, M. Naureen and S. Lee. Compressive sensing: form theory to applications, a survey, Journal of Communications and Networks, vol. 15, no. 5, pp. 443-456, Oct. 2013. [5] D. Baron, M.B. Wakin, M.F. Duarte, S. Sarvotham, and R.G. Baraniuk,“Distributed compressed sensing,” 2005, Preprint. [6] E. Candes, The restricted isometry property and its implications for compressed sensing, Comptes Rendus Mathematique, vol. 346, no. 9-10, pp. 589-592, 2008. [7] E. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inform. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. [8] Liang, K., Li, S., Zhang, W. et al. ”Reconstruction of enterprise debt networks based on compressed sensing”. Sci Rep 13, 2514 (2023). [9] S. G. Mallat and Zhifeng Zhang, "Matching pursuits with time-frequency dictionaries," in IEEE Transactions on Signal Processing, vol. 41, no. 12, pp. 3397-3415, Dec. 1993. [10] Jackson, John David, 1925-2016. (1999). ”Classical electrodynamics”. New York :Wiley. [11] GIBBS, J. Fourier''s Series. Nature 59, 200 (1898). [12] Jian-Jiun Ding, Time frequency analysis and wavelet transform class note, the Department of Electrical Engineering, National Taiwan University (NTU), Taipei, Taiwan, 2007. [13] Jian-Jiun Ding, Advanced Digital Signal Processing class note, the Department of Electrical Engineering, National Taiwan University (NTU), Taipei, Taiwan, 2007. [14] Jian-Jiun Ding, Selected Topics in Engineering Mathematics class note, the Department of Electrical Engineering, National Taiwan University (NTU), Taipei, Taiwan, 2007. [15] Jain, A. K. Fundamentals of Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989. [16] S. A. Martucci, "Symmetric convolution and the discrete sine and cosine transforms," IEEE Trans. Sig. Processing SP-42, 1038-1051 (1994). [17] Boggess, A. and Narcowich, F.J, “A First Course in Wavelets with Fourier Analysis”. John Wiley and Sons, Hoboken, 2001. [18] B. P. Lathi, Signal Processing & Linear Systems, Berkeley Cambridge Press, 1998. [19] J. Scott Tyo, Andrey S. Alenin, Field Guide to Linear Systems in Optics, Bellingham: SPIE, 2015. [20] [Untitled illustration of puppy cat]. Petboos. https://i.guim.co.uk/img/media/26392d05302e02f7bf4eb143bb84c8097d09144b/446_167_3683_2210/master/3683.jpg?width=1200&quality=85&auto=format&fit=max&s=a52bbe202f57ac0f5ff7f47166906403 [21] [Untitled illustration of forest]. Isearchlab. https://www.hilltimes.com/wp-content/uploads/2023/05/bryce-evans-choc7LYd98I-unsplash-e1684170248584-1200x720.jpg [22] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992. [23] Shaobing Chen and D. Donoho, Basis pursuit, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 1994. [24] Yi-Min Yang & Chieh-Hsiung Kuan PhD, Algorithm for building variable bandwidth with Fourier series, Master thesis, Graduate Institute of Photonics and Optoelectronics, National Taiwan University (NTU), Taipei, Taiwan, 2022. [25] Ban-Hoe Kwan and R. Paramesran, "Comparison between Legendre moments and DCT in ECG compression," 2004 IEEE Region 10 Conference TENCON 2004., Chiang Mai, Thailand, 2004, pp. 167-170 Vol. 1, doi: 10.1109/TENCON.2004.1414383. | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92071 | - |
dc.description.abstract | 在日常生活中,分段連續訊號無所不在,例如生物醫學訊號(心電訊號)、數位影像訊號、半導體測量訊號等。然而,此類訊號,特別是在奇異點(singular point)附近的訊號,特別難近似,常常會出現失真或需要過多的儲存資源。
因此在本篇論文中,我們採用了時頻分析和基於基底擴展的訊號處理的概念,提出了一種基於訊號分段連續性的分類演算法,對訊號進行預處理並將其分割為高頻區間和低頻區間;隨後,我們還提出了三種對於這些分段信號做相對應處裡的信號壓縮方式。 最後,我們建立了一個測試壓縮方法的平台,使用累積合比(Cumulative Sum ratio)作為信號經壓縮後,還原能力的評斷依據(evaluation criteria),並使用20種壓縮方法和我們所提出的三種方法做比較,並加入權重排名機制(weighted ranking)使比較更具參考價值,由最後的測試結果可看出,我們提出的壓縮方法是可以應用於準確的尋找ECG信號R峰值(R peak)區間和影像信號的壓縮。 | zh_TW |
dc.description.abstract | In daily life, piecewise continuous signals are ubiquitous, including biomedical signals (ECG signals), digital image signals, semiconductor measurement signals, etc. However, these signals, especially in the location near singular points, often suffer from distortion due to approximation difficulties or require excessive storage resources.
In this thesis, we employ the concepts of time-frequency analysis and signal processing based on basis expansion. We propose a classification algorithm based on the piecewise continuity of signals to preprocess and segment them into high-frequency and low-frequency parts. Subsequently, we propose three methods for decomposing each segmented signal. Finally, we established a platform for testing compression methods, utilizing the Cumulative Sum ratio as the evaluation criterion for the signal''s restoration ability after compression. We compared 20 compression methods with the three methods we proposed, incorporating a weighted ranking mechanism for a fairer and more informative comparison. The final test results show that our proposed compression methods can accurately locate the R-peak intervals in biomedical ECG signals and compress one row of image signals. | en |
dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-03-04T16:22:59Z No. of bitstreams: 0 | en |
dc.description.provenance | Made available in DSpace on 2024-03-04T16:22:59Z (GMT). No. of bitstreams: 0 | en |
dc.description.tableofcontents | 誌謝 i
中文摘要 ii ABSTRACT iii CONTENTS iv LIST OF FIGURES ix LIST OF TABLES xvii Chapter 1 Background Review for Compressive Sensing 1 1.1 Compressive sensing 1 1.1.1 Sparsity 2 1.1.2 Incoherence sampling 3 1.1.3 Applications 5 Chapter 2 Review for Basis Expansion 7 2.1 Signal Analysis Using Fourier Series Basis 7 2.2 Matching Pursuit 7 2.2.1 Introduction 8 2.2.2 Dictionary and Atomic Decompositions 9 2.2.3 Decomposition Structure 11 2.2.4 Experiments 14 2.3 Orthogonal Matching Pursuit 16 2.3.1 Compared to Matching Pursuit 16 2.3.2 Decomposition Structure 17 2.3.3 Experiments 21 2.4 Basis Pursuit 22 2.4.1 Introduction 22 2.4.2 Compared to Matching Pursuit 23 Chapter 3 Precision Calculation 26 3.1 Background 26 3.1.1 Completeness 26 3.1.2 Orthogonal basis and Dependent basis 26 3.2 Experiment for Square Wave Approximation 29 3.2.1 Gaussian-based approximate square wave 30 3.2.2 Error function-based approximate square wave 31 3.2.3 Using orthogonal bases to expand approximate square wave 32 3.2.4 Adding dependent basis to expand approximate square wave 34 3.3 Basis Optimization 37 3.3.1 Basis Optimization process 38 3.3.2 Experiments 39 3.4 Our proposed methods 45 3.4.1 Piecewise continuous 48 3.4.2 Nearly piecewise continuous 50 3.4.3 Less-variant frequency distribution 52 Chapter 4 Simulation Results 57 4.1 Compared methods introduction 59 4.1.1 Time domain Expansion 59 4.1.2 Fourier series Expansion 59 4.1.3 Discreet Cosine/Sine Transform[15][16] 59 4.1.4 Legendre polynomials fitting[25] 61 4.1.5 Discrete Wavelet Transform[17][22] 62 4.1.6 Linear Interpolation[18] 63 4.1.7 Sinc Interpolation[19] 64 4.1.8 Cubic B-Spline[12] 64 4.2 Artificially generated signals test 67 4.2.1 Square wave 67 4.2.2 Sawtooth wave 70 4.2.3 Piecewise continuous function with noise 1 71 4.2.4 Piecewise continuous function with noise 2 74 4.3 Biomedical signal---ECG signal 78 4.3.1 ECG signal test 1 78 4.3.2 ECG signal test 2 82 4.3.3 ECG signal test 3 85 4.3.4 ECG signal test 4 87 4.3.5 ECG signal test 5 88 4.3.6 ECG signal test 6 90 4.3.7 ECG signal test 7 91 4.4 Media signal(one row of image signal) 93 4.4.1 One row of image signal test 1 93 4.4.2 One row of image signal test 2 96 4.4.3 One row of image signal test 3 100 4.4.4 One row of image signal test 4 102 4.4.5 One row of image signal test 5 105 4.4.6 One row of image signal test 6 107 4.4.7 One row of image signal test 7 109 4.4.8 One row of image signal test 8 111 4.4.9 One row of image signal test 9 113 4.4.10 One row of image signal test 10 115 4.4.11 One row of image signal test 11 117 4.4.12 One row of image signal test 12 119 Chapter 5 Summary and Conclusions 121 REFERENCE 126 | - |
dc.language.iso | en | - |
dc.title | 透過精確計算對分段連續訊號進行高效率的基底擴展 | zh_TW |
dc.title | Efficient Piecewise Continuous Signal Basis Expansion by Precision Calculation | en |
dc.type | Thesis | - |
dc.date.schoolyear | 112-1 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 丁建均;劉俊麟;郭景明 | zh_TW |
dc.contributor.oralexamcommittee | Jian-Jiun Ding;Chun-Lin Liu;Jing-Ming Guo | en |
dc.subject.keyword | 精準計算,分段連續信號,信號壓縮,累積合比,ECG 信號 R 峰值, | zh_TW |
dc.subject.keyword | Precision Calculation,Piecewise Continuous Signal,Signal Compression,Cumulative Sum ratio,R-peak of ECG signal, | en |
dc.relation.page | 128 | - |
dc.identifier.doi | 10.6342/NTU202400387 | - |
dc.rights.note | 同意授權(全球公開) | - |
dc.date.accepted | 2024-02-16 | - |
dc.contributor.author-college | 重點科技研究學院 | - |
dc.contributor.author-dept | 元件材料與異質整合學位學程 | - |
顯示於系所單位: | 元件材料與異質整合學位學程 |
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