全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

能量泛函正则化模型在图像恢复中的应用分析

DOI: 10.11834/jig.20140901

Keywords: 图像恢复,正则化模型,偏微分方程,能量泛函

Full-Text   Cite this paper   Add to My Lib

Abstract:

目的能量泛函正则化模型是图像恢复研究的热点。为使更多工程领域的研究者对正则化技术进行探索和应用,推动不适定问题的研究,对能量泛函正则化模型的进展进行了分析。方法首先建立图像整体坐标与局部坐标的关系,分析图像恢复正则化模型的基本原理,给出并证明正则化模型各向同性与各向异性扩散定理。然后结合函数空间、图像分解和紧框架,评述能量泛函正则化模型国内外发展现状,并对正则化模型解的适定性进行分析。结果推导出图像恢复正则化模型扩散基本原理,给出正则化模型通用表达式,讨论正则化模型存在的问题及未来的发展方向。结论正则化技术在解决图像恢复、修复等反问题起着重要作用。目前,国内外学者对该问题的研究取得了一些成果,但许多理论问题有待进一步研究。

References

[1]  Issa S, Jazar M, Hamidi A EI. Ill-posedness of sublinear minimization problems [J]. Journal of the Egyptian Mathematical Society, 2011, 19(1-2): 88-90.
[2]  Aubert G, Hamidi A EI, Ghannam C, et al. On a class of ill-posed minimization problems in image processing [J]. Journal of Mathematical Analysis and Applications, 2009, 352(1): 380-399.
[3]  Wu T T, Yang Y F, Pang Z F. A modified fixed-point iterative algorithm for image restoration using fourth-order PDE model [J]. Applied Numerical Mathematics, 2012, 62(2): 79-90.
[4]  Haddad A, Meyer Y. An improvement of Rudin-Osher-Fatemi model [J]. Applied and Computational Harmonic Analysis, 2007, 22(3): 319-334.
[5]  Chen Y, Levine S, Rao M. Variable exponent, linear growth functionals in image restoration [J]. SIAM Journal on Applied Mathematics, 2006, 66(4): 1383-1406.
[6]  Fang H Z, Yan L X. Parametric blind deconvolution for passive millmeter wave images with framelet regularization[J]. International Journal for Light and Electron Optics, 2014, 125(3): 1454-1460.
[7]  Lin J H, Li S. Convergence of projected landweber iteration for matrix rank minimization [J]. Applied and Computational Harmonic Analysis, 2014, 36(2):316-325.
[8]  Hamidi A EI, Menard M, Lugiez M, et al. Weighted and extended total variation for image restoration and decomposition[J]. Pattern Recognition, 2010, 43(4):1564-1576.
[9]  Evans Lawrence C. Partial Differential Equations [M]. USA: American Mathematical Society, 1998.
[10]  Xiao L, Huang L L, Wei Z H. Comments on "staircase effect alleviation by coupling gradient fidelity term" [J]. Image and Vision Computing, 2010, 28(11):1569-1574.
[11]  Jia R Q, Zhao W. Riesz bases of wavelets and applications to numerical solutions of elliptic equations [J]. Mathematics of Computation, 2011, 80(275): 1525-1556.
[12]  Aubert G, Kornprobst P. Mathematical Problems in Image Processing: Partial Differential Equation and Calculus of Variations [M]. New York:Applied mathematical sciences, Springer Verlag, 2006.
[13]  Litvnov W G, Rahman T, Tai X C. A modified TV-stokes model for image processing [J]. SIAM Journal of Scientific Computing, 2011, 33(4): 1574-1597.
[14]  Wu B, Wu Y D, Zhang H Y. Image restoration based on partial differential equation[M]. Beijing: Peking University Press, 2008. [吴斌, 吴亚东, 张红英. 基于变分偏微分方程的图像复原技术[M]. 北京:北京大学出版社, 2008. ]
[15]  Jiao L C, Hou B, Wang S, et al. Image Multiscale Geometric Analysis: Theory and Applications, Beyond Wavelets[M]. Xi\'an: Xi\'an Electronic Science and Technology University Press, 2008. [焦李成, 侯彪, 王爽, 等. 图像多尺度几何分析理论与应用――后小波分析理论与应用[M]. 西安:西安电子科技大学出版社, 2008. ]
[16]  Jiang L L, Feng X C, Yin H Q. Image decomposition using optimally sparse representations and a variational approach [J]. Signal, Image and Video Processing, 2007, 1(4): 287-292.
[17]  Zhang J, Wang C, Cheng Y. Despeckling for medical ultrasound images based on wavelet and bilateral filter [J]. Journal of Image and Graphics, 2014, 19(1):126-132. [张聚, 王陈, 程芸. 小波域双边滤波的医学超声图像去噪 [J]. 中国图象图形学报, 2014, 19(1):126-132. ][DOI:10.11834/jig.20140116]
[18]  Fei X, Wei Z H, Xiao L, et al. Compound regularized compressed sensing image reconstruction based on optimal reweighted TV [J]. Journal of Image and Graphics, 2014, 19(2):211-218. [费选, 韦志辉, 肖亮, 等. 优化加权TV的复合正则化压缩感知图像重建[J]. 中国图象图形学报, 2014, 19(2):211-218. ][DOI:10.11834/jig.20140206]
[19]  Bai Z J, Donatelli M, Capizzano S S. Fast preconditioners for total variation deblurring with anti-reflective boundary conditions [J]. SIAM Journal on matrix analysis and applications, 2011, 32(3): 785-805.
[20]  Neubauer A. Tikhonov regularization of nonlinear ill-posed problems in Hilbert scales [J]. Applicable Analysis, 1992, 46(2): 59-72.
[21]  更多...
[22]  Lysaker M, Tai X C. Iterative image restoration combining total variation minimization and a second-order functional [J]. International Journal of Computer Vision, 2006, 66(1): 5-18.
[23]  Liu X W, Huang L H, Guo Z Y. Adaptive fourth-order partial differential equation filter for image denoising [J]. Applied Mathematics Letters, 2011, 24(8):1282-1288.
[24]  Jiang Q T. Correspondence between frame shrinkage and high-order nonlinear diffusion [J]. Applied and Computational Harmonic Analysis, 2012, 6(1):51-66.
[25]  Li F, Li Z B, Pi L. Variable exponent functionals in image restoration [J]. Application Mathematics and Compution, 2010, 216(3): 870-882.
[26]  Meyer Yves. Oscillating Patterns in Image Processing and Nonlinear Evolution Equations [M]. USA: AMS, 2001.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133