Half-Quadratic Algorithm for $$\ell _p$$ - $$\ell _q$$ Problems with Applications to TV- $$\ell _1$$ Image Restoration and Compressive Sensing

作者: Raymond H. Chan , Hai-Xia Liang

DOI: 10.1007/978-3-642-54774-4_4

关键词: PhysicsMinimization problemQuadratic equationCompressed sensingAlgorithmMonotonic functionImage restorationMr images

摘要: … and compressive sensing. In the paper, we first extend the half-quadratic algorithm from \(\… Based on this, we develop a half-quadratic algorithm to solve the \(\ell _p\)-\(\ell _q\) problem…

参考文章(47)
Wotao Yin, Donald Goldfarb, Stanley Osher, The Total Variation Regularized L1 Model for Multiscale Decomposition Defense Technical Information Center. ,(2006) , 10.21236/ADA460529
Ivar Ekeland, Roger Téman, Convex analysis and variational problems ,(1976)
Wotao Yin, Donald Goldfarb, Stanley Osher, Image cartoon-texture decomposition and feature selection using the total variation regularized L 1 functional Lecture Notes in Computer Science. pp. 73- 84 ,(2005) , 10.1007/11567646_7
Mila Nikolova, Raymond H. Chan, The Equivalence of Half-Quadratic Minimization and the Gradient Linearization Iteration IEEE Transactions on Image Processing. ,vol. 16, pp. 1623- 1627 ,(2007) , 10.1109/TIP.2007.896622
Tony F. Chan, H. M. Zhou, Raymond H. Chan, Continuation method for total variation denoising problems conference on advanced signal processing : algorithms, architectures, and implemenations. ,vol. 2563, pp. 314- 325 ,(1995) , 10.1117/12.211408
Junfeng Yang, Yin Zhang, Wotao Yin, An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise SIAM Journal on Scientific Computing. ,vol. 31, pp. 2842- 2865 ,(2009) , 10.1137/080732894
G. Hosein Mohimani, Massoud Babaie-Zadeh, Christian Jutten, Fast Sparse Representation Based on Smoothed ℓ0 Norm Independent Component Analysis and Signal Separation. pp. 389- 396 ,(2007) , 10.1007/978-3-540-74494-8_49
Wotao Yin, Stanley Osher, Donald Goldfarb, Jerome Darbon, Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing Siam Journal on Imaging Sciences. ,vol. 1, pp. 143- 168 ,(2008) , 10.1137/070703983
D. Geman, Chengda Yang, Nonlinear image recovery with half-quadratic regularization IEEE Transactions on Image Processing. ,vol. 4, pp. 932- 946 ,(1995) , 10.1109/83.392335
Tony F. Chan, Selim Esedoglu, Aspects of Total Variation Regularized L1 Function Approximation Siam Journal on Applied Mathematics. ,vol. 65, pp. 1817- 1837 ,(2005) , 10.1137/040604297