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| Medical Image Deconvolution in Besov Space Based on Sparse Decomposition |
| WEN Qiao-Nong1 ,XU Shuang2 ,WAN Sui-Ren1 |
1. Medical Electronics Laboratory,Southeast University,Nanjing 210096
2.Laboratory of Image Science and Technology,Southeast University,Nanjing 210096 |
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Abstract In the framework of sparse decomposition, an image deconvolution functional variation model in the Besov smooth space is proposed. The data item is constrained in the negative Hilbert-Sobolev space, while the regularization item is constrained by sparsity and smoothness. Both the sparsity and the smoothness are taken into account by regarding the L1 norm of the redundant dictionary as a sparsity measure and semi-norm as image smoothness measure in Besov space. The operator splitting method is adopted due to the difficulty in solving this mode directly. The original model is split into two parts: image deconvolution and sparse decomposition. Thus, it is solved using cross-iterative method. The resolution of the model pseudo-code is given in detail and the convergence of the algorithm is verified experimentally. The results show that deconvolution model is better than other models.
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Received: 27 October 2010
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[1] Dupe F X,Fadili J M,Starck J L.A Proximal Iteration for Deconvolving Poisson Noisy Images Using Sparse Representations.IEEE Trans on Image Processing,2009,18(2): 310-321
[2] Scholefield A,Dragotti P L.Image Restoration Using a Sparse Quadtree Decomposition Representation // Proc of the 16th IEEE International Conference on Image Processing.Cairo,Egypt,2009: 1473-1476
[3] Deka B,Bora P K.Despeckling of Medical Ultrasound Images Using Sparse Representation // Proc of the 4th International Conference on Signal Processing and Communication Systems.Gold Coast,Australia,2010: 1-5
[4] Adler A,Yacov H O,Elad M.A Shrinkage Learning Approach for Single Image Super-Resolution with Overcomplete Representations // Proc of the 11th European Conference on Computer Vision.Heraklion,Greece,2010: 622-635
[5] Michael E,Figueiredo M A T,Yi M.On the Role of Sparse and Redundant Representations in Image Processing.Proc of IEEE,2010,98(6): 972-982
[6] Needell D,Vershynin R.Signal Recovery from Incomplete and Inaccurate Measurements via Regularized Orthogonal Matching Pursuit.IEEE Journal of Selected Topics in Signal Processing,2010,4(2): 310-316
[7] Chesneau C,Fadili M J,Starck J L.Image Deconvolution by Stein Block Thresholding // Proc of the 16th IEEE International Conference on Image Processing.Cairo,Egypt,2009: 1329-1332
[8] Dimitris G T,Aristidis C L,Nikolaos P G.Variational Bayesian Sparse Kernel-Based Blind Image Deconvolution with Students-t Priors.IEEE Trans on Image Processing,2009,18(4): 753-764
[9] Elad M.Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing.New York,USA: Springer-Verlag,2010
[10] Vonesch C,Unser M.A Fast Iterative Thresholding Algorithm for Wavelet Regularized Deconvolution // Proc of the 4th IEEE International Symposium on Biomedical Imaging: From Nano to Macro.Arlington,USA,2007: 608-611
[11] Pu Jian,Zhang Junping.Super-Resolution through Dictionary Learning and Sparse Representation.Pattern Recognition and Artificial Intelligence,2010,23(3): 335-341 (in Chinese)
(浦 剑,张军平.基于词典学习和稀疏表示的超分辨率重建.模式识别与人工智能,2010,23(3): 335-341)
[12] Osher S,Solé A,Vese L.Image Decomposition and Restoration Using Total Variation Minimization and the H-1 Norm.Multiscale Modeling Simulation,2004,1(3): 349-370
[13] Daubechies I,Teschke G.Wavelet Based Image Decomposition by Variational Functionals.Proc of SPIE,2004,5266: 94-105
[14] Jiang Lingling,Feng Xiangchu,Yin Haiqing.Variational Image Restoration and Decomposition with Curvelet Shrinkage.Journal of Mathematical Imaging and Vision,2008,30(2): 125-132
[15] Jiang Lingling,Feng Xiangchu,Yin Haiqing.Blind Image Restoration Algorithm Based on Besov Spaces.Journal of Data Acquisition Processing,2008,23(6): 678-682 (in Chinese)
(江玲玲,冯象初,殷海青.基于Besov空间的图像盲复原算法.数据采集与处理,2008,23(6): 678-682)
[16] Linh H L,Luminita A V.Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces.Applied Mathematics Optimization,2008,58(2): 167-193 |
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2012, Vol. 25 
