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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 陳宜良 | |
dc.contributor.author | Yi-Man Tseng | en |
dc.contributor.author | 曾怡滿 | zh_TW |
dc.date.accessioned | 2021-06-15T06:00:07Z | - |
dc.date.available | 2010-08-20 | |
dc.date.copyright | 2010-08-20 | |
dc.date.issued | 2010 | |
dc.date.submitted | 2010-08-16 | |
dc.identifier.citation | [1] A. Chambolle, An algorithm for total variation minimization and applications,
Journal of Mathematical Imaging and Vision, 20 (2004), pp. 89–97. [2] S. G. Chang, B. Yu, and M. Vetterli, Adaptive wavelet thresholding for image denoising and compression, IEEE Transacions on Image Processing, 9 (2000), pp. 1532–1546. [3] I. Daubechies, Ten lectures on Wavelets, SIAM: Society for Industrial and Applied Mathematics, 1 ed., 1992. [4] D. L. Donoho, De-noising by soft-thresholding, IEEE Transactions on Infor- mation Theory, 41 (1995), pp. 613–627. [5] D. L. Donoho and I. M. Johnstone, Adapting to unknown smoothness via wavelet shrinkage, Journal of the American Statistical Association, 90 (1995), pp. 1200–1224. [6] T. Le, R. Chartrand, and T. J. Asaki, A variational approach to recon- structing images corrupted by poisson noise, Journal of Mathematical Imaging and Vision, 27 (2007), pp. 257–263. [7] S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press, 3 ed., 2008. [8] L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp. 259–268. [9] T. Sun and Y. Neuvo, Detail-preserving median based filters in image pro- cessing, Pattern Recongnition Letters, 15 (1994), pp. 341–347. | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/47444 | - |
dc.description.abstract | We propose to review four common types of image noises, including Gaussian noise, uniform noise, Poisson noise and salt & pepper noise. We set basic one-dimensional and two-dimensional images, and add four types of noises on different levels. We will denoise these corrupted images by using total variation, soft-thresholding and adaptive median filter, respectively. Finally, compare the PSNR values to analyse the denoising effect, edges preserving, and blurring. | en |
dc.description.provenance | Made available in DSpace on 2021-06-15T06:00:07Z (GMT). No. of bitstreams: 1 ntu-99-R95221023-1.pdf: 1507218 bytes, checksum: c81317ce3b1b843d3d7f89ffe18233e9 (MD5) Previous issue date: 2010 | en |
dc.description.tableofcontents | Contents
Abstract i 1 Introduction 1 2 Mathematical Models 2 2.1 Basic Image and Noise Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Uniform noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Poisson Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Salt & Pepper Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Denoise Techniques 8 3.1 TV Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Wavelet Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Soft-Thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Adaptive Median Filter Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4 Numerical Results 18 4.1 TV Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.1.1 Gaussian noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.1.2 Uniform noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.1.3 Poisson noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Denoising by Thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2.1 Gaussian noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2.2 Uniform noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.2.3 Poisson noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3 Adaptive Median Filter Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3.1 salt & pepper noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5 Conclusion 30 Reference 31 List of Figures 1 (a)1-D, (b)2-D original image with 8 pixels between two figures. . . . . . . . . . . . . 3 2 1-D and 2-D images corrupted by Gaussian noises with mean 0 and variance (a)(c) 0.01, (b)(d) 0.05. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 1-D and 2-D images corrupted by uniform noises with noise bound: (a)(c) ±0.2, (b)(d) ±0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 1-D and 2-D images corrupted by Poisson noises with (a)(c) τ= 0.01, (b)(d) τ = 0.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5 1-D and 2-D images corrupted by salt & pepper noises with noise ratio (a)(c) 0.1, (b)(d) 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 6 Daubechies5 scaling and wavelet function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7 TV denoising for Gaussian noise. The distance between two figures are 4 pixels(left) and 8 pixels(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 8 TV denoising for uniform noise. The distance between two figures are 4 pixels(left) and 8 pixels(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 9 TV denoising for Poisson noise. The distance between two figures are 4 pixels(left) and 8 pixels(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 10 Soft-thresholding for Gaussian noise after Daubechies 5 wavelet transform. The distance between two figures are 4 pixels (left) and 8 pixels (right). . . . . . . . 22 11 Soft-thresholding for uniform noise after Daubechies 5 wavelet transform. The distance between two figures are 4 pixels(left) and 8 pixels(right). . . . . . . . 23 12 Soft-thresholding for Poisson noise after Daubechies 5 wavelet transform. The distance between two figures are 4 pixels(left) and 8 pixels(right). . . . . . . . . . 24 13 Adaptive median filter denoising for salt & pepper noise. The distance between two figures are 4 pixels(left) and 8 pixels(right). . . . . . . . . . . . . . . . . . 25 List of Tables 1 PSNR values of images corrupted by Gaussian noise and denoised images. (σ2 : variance, λ : regularization parameter, T : threshold) . . . . . . . . . . . . . . . . . . . 26 2 PSNR values of images corrupted by uniform noise and denoised images. (B : noise bound, λ: regularization parameter, T : threshold) . . . . . . . . . . . . . . . . . 27 3 PSNR values of images corrupted by Poisson noise and denoised images. (τ : image quantization unit, λ : regularization parameter, T : threshold) . . . . . . . .28 4 PSNR values of images corrupted by salt & pepper noise and denoised images. (r : noise ratio, w : window size, AMF : adaptive median filter) . . . . . . . . . . . . . 29 | |
dc.language.iso | en | |
dc.title | 雜訊模式與去雜訊方法 | zh_TW |
dc.title | Noise Models and Denoising Techniques | en |
dc.type | Thesis | |
dc.date.schoolyear | 98-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 王偉成,曾正男 | |
dc.subject.keyword | 去雜訊,小波,全變差,軟式閾值,適應性中間值濾波器, | zh_TW |
dc.subject.keyword | Denoising,Wavelet,Soft-thresholding,TV,Adaptive Median Filter, | en |
dc.relation.page | 32 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2010-08-17 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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