臺灣博碩士論文加值系統

本篇碩士論文的目的是在面對混合雜訊的圖像處理上，利用了Hintermuller et al., 2013所提出的模型並加以改良。而原始模型是以Rudin-Osher-Fatemi (ROF) model為基礎並將兩項資料項結合而形成的，且在面對混合雜訊的圖像處理上比原始單一雜訊的模型都還要來的好，但是由於模型的正規項|nabla u|易造成階梯效應的狀況產生(缺點和傳統ROF model同)，過去利用增加|nabla u|^2(平方項)來降低此效應。而我們將透過引入一個自適應性算子(此算子在q=1、2時分別具有保邊及平滑的功用)，對此模型做改良並期待一樣能減緩階梯效應情況。藉由一系列的數值實驗結果呈現，引入的自適應性算子很成功地發揮出效用，不僅僅具有降低階梯效應情況且額外多了保邊的功效。

The purpose of this thesis is to develop an effective variational model for mixed
noise removal. The newly proposed model is based on the one in [8] but with an adaptive
regularization term α_{p,q}, 0 < p ≤ 1, q = 1 or 2. The adaptive regularization can have the
ability to preserve the edge structure of the image and also alleviate the staircase effect
of the image. From the numerical experiments, we will find that the proposed model has
good performance for sharpening edges and restoring images.

摘要 i
Abstract ii
目次 iii
表目次 iv
圖目次 v
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 3
第二章 相關研究探討及實驗方法 4
2.1. HL-model 4
2.2. JSZW-model 7
2.3. HSY-operator 8
2.4. 模型證明-實驗方法 11
第三章 實驗結果 17
3.1. Example 1 19
3.2. Example 2 23
3.3. Example 3 29
第四章 結論 33
參考文獻 34

[1]W. K. Allard, Total variation regularization for image denoising, I.Geometric theory, SIAM Journal on Mathematical Analysis, Vol.39, No.4, pp.1150–1190, 2007.

[2]A. Buades, B. Coll and J. M. Morel, A review of image denoising algorithms with a new one, Multiscale Modeling & Simulation, Vol.4, No.2, pp.490–530, 2005.

[3]X. Cai, R. Chan and T. Zeng, A two-stage images segmentation method using a convex variant of the Mumford-Shah model and thresholding, SIAM Journal on Imaging Science, Vol.6, No.1, pp.368–390, 2013.

[4]D. L. Donoho, De-noising by soft-thresholding, IEEE Transaction on information Theory, Vol.40, No.3, pp.613–627, 1995.

[5]P. Getreuer, Rudin-Osher-Fatemi Total Variation Denoising using Split Bregman, it Image Processing On Line, Vol.2, pp.74–95, 2012.

[6]G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Modeling & Simulation, Vol.7, No.3, pp.1005–1028, 2008.

[7]T. Goldstein and S. Osher, The split Bregman method for L1-regularized problems, SIAM Journal on Imaging Sciences, Vol.2, No.2, pp.323–343, 2009.

[8]M. Hintermuller and A. Langer, Subspace correction methods for a class of non-smooth and non-additive convex variational problems with mixed L^1/L^2 data-fidelity in image processing, SIAM Journal on Imaging Sciences, Vol.6, No.4, pp.2134–2173, 2013.

[9]P.-W. Hsieh, P.-C. Shao and S.-Y. Yang, A regularization model with adaptive diffusivity for variational image denoising, Signal Processing, Vol.149, pp.214–228, 2018.

[10]T. Jia, Y. Shi, Y. Zhu and L. Wang, An image restoration model combining mixed L^1/L^2 fidelity terms, Journal of Visual Communication and Image Representation Vol.38, pp. 461–473, 2016.

[11]Y. Li and Z. Huang, Efficient schemes for joint isotropic and anisotropic total variation minimization for deblurring images corrupted by impulsive noise, Computers & Graphics, Vol.38, pp.108–116, 2014.

[12]G. Liu, T.-Z. Huang and J. Liu, High-order TVL1-based images restoration and spatially adapted regularization parameter selection, Computers and Mathematics with Applications, Vol.67, No.10, pp.2015–2026, 2014.

[13]Y. Lou, X. Zhang, S. Osher and A. Bertozzi, Image Recovery via Nonlocal Operators, Journal of Scientific Computing, Vol.42, No.2, pp.185–197, 2010.

[14]L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, Vol.60, No.1-4, pp.259–268, 1992.

[15]Y. Shi and Q. Chang, Efficient Algorithm for Isotropic and Anisotropic Total Variation Deblurring and Denoising, Journal of Applied Mathematics,Vol.2013, pp.1-4, 2013.