[1] Zhang Tao, Wei Haiguang, Mo Xutao,. Image denoising method with tree-structured group sparsemodeling of wavelet coefficients [J]. Journal of Southeast University (English Edition), 2019, 35 (3): 332-340. [doi:10.3969/j.issn.1003-7985.2019.03.009]
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Image denoising method with tree-structured group sparsemodeling of wavelet coefficients(
)
基于小波系数树状结构的组稀疏图像去噪方法
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 35
- Issue:
- 2019 3
- Page:
- 332-340
- Research Field:
- Image Processing
- Publishing date:
- 2019-09-30
Info
- Title:
- Image denoising method with tree-structured group sparsemodeling of wavelet coefficients
- 基于小波系数树状结构的组稀疏图像去噪方法
- Author(s):
- Zhang Tao, Wei Haiguang, Mo Xutao
- School of Mathematics and Physics, Anhui University of Technology, Ma’anshan 243000, China
- Keywords:
- local standard deviation; group sparse; image denoising; mixed norm; texture
- PACS:
- TP751
- DOI:
- 10.3969/j.issn.1003-7985.2019.03.009
- Abstract:
- In order to enhance the image contrast and quality, inspired by the interesting observation that an increase in noise intensity tends to narrow the dynamic range of the local standard deviation(LSD)of an image, a tree-structured group sparse optimization model in the wavelet domain is proposed for image denoising. The compressed dynamic range of LSD caused by noise leads to a contrast reduction in the image, as well as the degradation of image quality. To equalize the LSD distribution, sparsity on the LSD matrix is enforced by employing a mixed norm as a regularizer in the image denoising model. This mixed norm introduces a coupling between wavelet coefficients and provides a tree-structured group scheme. The alternating direction method of multipliers(ADMM)and the fast iterative shrinkage-thresholding algorithm(FISTA)are applied to solve the group sparse model based on different cases. Several experiments are conducted to verify the effectiveness of the proposed model. The experimental results indicate that the proposed group sparse model can efficiently equalize the LSD distribution and therefore can improve the image contrast and quality.
- 为了提高图像对比度以及图像质量, 受图像的局部均方差变化范围会随噪声强度的增强而变窄这一有趣的现象启发, 在小波域中提出了一种基于小波系数树状结构的组稀疏图像去噪模型.由噪声导致的图像局部均方差变化范围的压缩会引起图像对比度以及图像质量的下降.为了平衡图像的局部均方差分布, 引入一种混合范数作为图像去噪模型的正则项, 以达到对局部均方差矩阵进行稀疏约束的目的.该混合范数引入了小波系数之间的耦合, 并且给出了一种小波系数的树状分组方式.利用交替方向乘子法(ADMM)以及快速迭代阈值收缩算法(FISTA)研究模型在不同情况下的求解方法.最后, 通过多组实验验证了所提模型的有效性.实验结果表明, 提出的组稀疏优化模型能够有效地平衡图像的局部均方差分布, 从而提高图像的对比度和图像质量.
References:
[1] Tikhonov A N. Regularization of incorrectly posed problems [J]. Soviet Mathematics Doklady, 1963, 4: 1624-1627.
[2] Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms[J].Physica D: Nonlinear Phenomena, 1992, 60(1/2/3/4): 259-268. DOI:10.1016/0167-2789(92)90242-f.
[3] Buades A, Coll B, Morel J M. Nonlocal image and movie denoising[J].International Journal of Computer Vision, 2008, 76(2): 123-139. DOI:10.1007/s11263-007-0052-1.
[4] Ding D, Ram S, Rodriguez J J. Image inpainting using nonlocal texture matching and nonlinear filtering[J].IEEE Transactions on Image Processing, 2019, 28(4): 1705-1719. DOI:10.1109/tip.2018.2880681.
[5] Wang W, Li F, Ng M K. Structural similarity-based nonlocal variational models for image restoration[J].IEEE Transactions on Image Processing, 2019, 28(9): 4260-4272. DOI:10.1109/tip.2019.2906491.
[6] Zhang K, Zuo W, Chen Y J, et al. Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising[J].IEEE Transactions on Image Processing, 2017, 26(7): 3142-3155. DOI:10.1109/tip.2017.2662206.
[7] Jin K H, McCann M T, Froustey E, et al. Deep convolutional neural network for inverse problems in imaging[J].IEEE Transactions on Image Processing, 2017, 26(9): 4509-4522. DOI:10.1109/tip.2017.2713099.
[8] Starck J L, Elad M, Donoho D L. Image decomposition via the combination of sparse representations and a variational approach[J].IEEE Transactions on Image Processing, 2005, 14(10): 1570-1582. DOI:10.1109/tip.2005.852206.
[9] Cai J F, Osher S, Shen Z. Split bregman methods and frame based image restoration[J].Multiscale Modeling & Simulation, 2010, 8(2): 337-369. DOI:10.1137/090753504.
[10] Dong W S, Shi G M, Ma Y, et al. Image restoration via simultaneous sparse coding: Where structured sparsity meets Gaussian scale mixture[J].International Journal of Computer Vision, 2015, 114(2/3): 217-232. DOI:10.1007/s11263-015-0808-y.
[11] Zhang L, Zuo W. Image restoration: From sparse and low-rank priors to deep priors[J].IEEE Signal Processing Magazine, 2017, 34(5): 172-179. DOI:10.1109/msp.2017.2717489.
[12] Zhang J, Zhao D, Gao W. Group-based sparse representation for image restoration[J].IEEE Transactions on Image Processing, 2014, 23(8): 3336-3351. DOI:10.1109/tip.2014.2323127.
[13] Kowalski M. Sparse regression using mixed norms[J].Applied and Computational Harmonic Analysis, 2009, 27(3): 303-324. DOI:10.1016/j.acha.2009.05.006.
[14] Yang J Q, Zhu G P, Shi Y Q. Analyzing the effect of JPEG compression on local variance of image intensity[J].IEEE Transactions on Image Processing, 2016, 25(6): 2647-2656. DOI:10.1109/tip.2016.2553521.
[15] Li Z G, Zeng L, Xu Y F, et al. Level set method for image segmentation based on local variance and improved intensity inhomogeneity model[J].IET Image Processing, 2016, 10(12): 1007-1016. DOI:10.1049/iet-ipr.2016.0352.
[16] Meyer Y. Wavelet and operators [M].Cambridge: Cambridge University Pressing, 1992: 21-25.
[17] Zhang T, Fan Q B. Wavelet characterization of dyadic BMO norm and its application in image decomposition for distinguishing between texture and noise[J]. International Journal of Wavelets, Multiresolution and Information Processing, 2011, 9(3): 445-457. DOI:10.1142/s0219691311004183.
[18] Boyd S. Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations and Trends�A9; in Machine Learning, 2010, 3(1): 1-122. DOI:10.1561/2200000016.
[19] Beck A, Teboulle M. Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems[J].IEEE Transactions on Image Processing, 2009, 18(11): 2419-2434. DOI:10.1109/tip.2009.2028250.
Memo
- Memo:
-
Biography: Zhang Tao(1982— ), male, doctor, associate professor, zt9877@163.com.
Foundation items: The National Natural Science Foundation of China(No.61701004, 11504003), the Natural Science Foundation of Anhui Province(No.1708085QA15).
Citation: Zhang Tao, Wei Haiguang, Mo Xutao.Image denoising method with tree-structured group sparse modeling of wavelet coefficients[J].Journal of Southeast University(English Edition), 2019, 35(3):332-340.DOI:10.3969/j.issn.1003-7985.2019.03.009.