[1]
|
E. Altinsoy, J. Yang and E. Tu, An improved denoising of G-banding chromosome images using cascaded CNN and binary classification network, The Visual Computer, 38 (2022), 2139-2152.
doi: 10.1007/s00371-021-02273-5.
|
[2]
|
L. Ambrosio and S. Masnou, A direct variational approach to a problem arising in image reconstruction, Interfaces and Free Boundaries, 5 (2003), 63-81.
doi: 10.4171/IFB/72.
|
[3]
|
J. Bai and X.-C. Feng, Fractional-order anisotropic diffusion for image denoising, IEEE Transactions on Image Processing, 16 (2007), 2492-2502.
doi: 10.1109/TIP.2007.904971.
|
[4]
|
K. Bredies, K. Kunisch and T. Pock, Total generalized variation, SIAM Journal on Imaging Sciences, 3 (2010), 492-526.
doi: 10.1137/090769521.
|
[5]
|
A. Chambolle and P.-L. Lions, Image recovery via total variation minimization and related problems, Numerische Mathematik, 76 (1997), 167-188.
doi: 10.1007/s002110050258.
|
[6]
|
T. F. Chan, S. Esedoglu and F. Park, A fourth order dual method for staircase reduction in texture extraction and image restoration problems, 2010 IEEE International Conference on Image Processing, 2010, 4137-4140.
doi: 10.1109/ICIP.2010.5653199.
|
[7]
|
R. H. Chan, H. Liang, S. Wei, M. Nikolova and X.-C. Tai, High-order total variation regularization approach for axially symmetric object tomography from a single radiograph, Inverse Problems and Imaging, 9 (2015), 55-77.
doi: 10.3934/ipi.2015.9.55.
|
[8]
|
T. Chan, A. Marquina and P. Mulet, High-order total variation-based image restoration, SIAM Journal on Scientific Computing, 22 (2000), 503-516.
doi: 10.1137/S1064827598344169.
|
[9]
|
C. Cruz, A. Foi, V. Katkovnik and K. Egiazarian, Nonlocality-reinforced convolutional neural networks for image denoising, IEEE Signal Processing Letters, 25 (2018), 1216-1220.
doi: 10.1109/LSP.2018.2850222.
|
[10]
|
J. Duan, Z. Qiu, W. Lu, G. Wang, Z. Pan and L. Bai, An edge-weighted second order variational model for image decomposition, Digital Signal Processing, 49 (2016), 162-181.
doi: 10.1016/j.dsp.2015.10.010.
|
[11]
|
G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Modeling and Simulation, 7 (2009), 1005-1028.
doi: 10.1137/070698592.
|
[12]
|
S. Goyal, V. Singh, A. Rani and N. Yadav, Multimodal image fusion and denoising in NSCT domain using CNN and FOTGV, Biomedical Signal Processing and Control, 71 (2022), 103214.
doi: 10.1016/j.bspc.2021.103214.
|
[13]
|
R. Kimmel, R. Malladi and N. Sochen, Images as embedded maps and minimal surfaces: Movies, color, texture, and volumetric medical images, International Journal of Computer Vision, 39 (2000), 111-129.
doi: 10.1023/A:1008171026419.
|
[14]
|
S. Lefkimmiatis and M. Unser, Poisson image reconstruction with Hessian Schatten-norm regularization, IEEE Transactions on Image Processing, 22 (2013), 4314-4327.
doi: 10.1109/TIP.2013.2271852.
|
[15]
|
S. Lefkimmiatis, J. P. Ward and M. Unser, Hessian Schatten-norm regularization for linear inverse problems, IEEE Transactions on Image Processing, 22 (2013), 1873-1888.
doi: 10.1109/TIP.2013.2237919.
|
[16]
|
F. Li, C. Shen, J. Fan and C. Shen, Image restoration combining a total variational filter and a fourth-order filter, Journal of Visual Communication and Image Representation, 18 (2007), 322-330.
doi: 10.1016/j.jvcir.2007.04.005.
|
[17]
|
J. Liu, R. W. Liu, J. Sun and T. Zeng, Rank-one prior: Real-time scene recovery, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022.
doi: 10.1109/CVPR46437.2021.01456.
|
[18]
|
W. Lu, J. Duan, Z. Qiu, Z. Pan, R. W. Liu and L. Bai, Implementation of high-order variational models made easy for image processing, Mathematical Methods in the Applied Sciences, 39 (2016), 4208-4233.
doi: 10.1002/mma.3858.
|
[19]
|
M. Lysaker, A. Lundervold and X.-C. Tai, Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time, IEEE Transactions on Image Processing, 12 (2003), 1579-1590.
doi: 10.1109/TIP.2003.819229.
|
[20]
|
X. Mao, C. Shen and Y. Yang, Image restoration using very deep convolutional encoder-decoder networks with symmetric skip connections, Advances in Neural Information Processing Systems, 29 (2016), 2802-2810.
|
[21]
|
S. Osher, A. Sole and L. Vese, Image decomposition and restoration using total variation minimization and the $H^{-1}$ norm, Multiscale Modeling and Simulation, 1 (2003), 349-370.
doi: 10.1137/S1540345902416247.
|
[22]
|
Z.-F. Pang, L.-Z. Guo, Y. Duan and J. Lu, Image restoration based on the minimized surface regularization, Computers and Mathematics with Applications, 76 (2018), 1893-1905.
doi: 10.1016/j.camwa.2018.07.037.
|
[23]
|
Z.-F. Pang, Y.-M. Zhou, T. Wu and D.-J. Li, Image denoising via a new anisotropic total-variation-based model, Signal Processing: Image Communication, 74 (2019), 140-152.
doi: 10.1016/j.image.2019.02.003.
|
[24]
|
K. Papafitsoros and C. B. Schonlieb, A combined first and second order variational approach for image reconstruction, Journal of Mathematical Imaging and Vision, 48 (2014), 308-338.
doi: 10.1007/s10851-013-0445-4.
|
[25]
|
Y. Quan, Y. Chen, Y. Shao, H. Teng, Y. Xu and H. Ji, Image denoising using complex-valued deep CNN, Pattern Recognition, 111 (2021), 107639.
doi: 10.1016/j.patcog.2020.107639.
|
[26]
|
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F.
|
[27]
|
O. Scherzer, Denoising with higher order derivatives of bounded variation and an application to parameter estimation, Computing, 60 (1998), 1-27.
doi: 10.1007/BF02684327.
|
[28]
|
X.-C. Tai, J. Hahn and G. J. Chung, A fast algorithm for Eulers Elastica model using augmented Lagrangian method, SIAM Journal on Imaging Sciences, 4 (2011), 313-344.
doi: 10.1137/100803730.
|
[29]
|
C. Tian, Y. Xu, W. Zuo, B. Du, C.-W. Lin and D. Zhang, Designing and training of a dual CNN for image denoising, Knowledge-Based Systems, 226 (2021), 106949.
doi: 10.1016/j.knosys.2021.106949.
|
[30]
|
L. A. Vese and S. J. Osher, Modeling textures with total variation minimization and oscillatory patterns in image processing, Journal of Scientific Computing, 19 (2003), 553-579.
doi: 10.1023/A:1025384832106.
|
[31]
|
G. Wang, J. Xu, Q. Dong and Z. Pan, Active contour model coupling with higher order diffusion for medical image segmentation, International Journal of Biomedical Imaging, 2014.
doi: 10.1155/2014/237648.
|
[32]
|
Y. Wang, J. Yang, W. Yin and Y. Zhang, A new alternating minimization algorithm for total variation image reconstruction, SIAM Journal on Imaging Sciences, 1 (2008), 248-272.
doi: 10.1137/080724265.
|
[33]
|
D. Yang and J. Sun, Bm3d-net: A convolutional neural network for transform-domain collaborative filtering, IEEE Signal Processing Letters, 25 (2017), 55-59.
doi: 10.1109/LSP.2017.2768660.
|
[34]
|
J. Yang, M. Ma, J. Zhang and C. Wang, Noise removal using an adaptive Euler's elastica-based model, The Visual Computer, 2022, 1-12.
doi: 10.1007/s00371-022-02674-0.
|
[35]
|
Y.-L. You and M. Kaveh, Fourth-order partial differential equations for noise removal, IEEE Transactions on Image Processing, 9 (2000), 1723-1730.
doi: 10.1109/83.869184.
|
[36]
|
J. Zhang, R. Chen, C. Deng and S. Wang, Fast linearized augmented Lagrangian method for Euler's elastica model, Numerical Mathematics: Theory, Methods and Applications, 10 (2017), 98-115.
doi: 10.4208/nmtma.2017.m1611.
|
[37]
|
J. Zhang and Z. Wei, A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising, Applied Mathematical Modelling, 35 (2011), 2516-2528.
doi: 10.1016/j.apm.2010.11.049.
|
[38]
|
W. Zhu, Image denoising using $L^p$-norm of mean curvature of image surface, Journal of Scientific Computing, 83 (2020), No. 32, 26 pp.
doi: 10.1007/s10915-020-01216-x.
|
[39]
|
W. Zhu and T. Chan, Image denoising using mean curvature of image surface, SIAM Journal on Imaging Sciences, 5 (2012), 1-32.
doi: 10.1137/110822268.
|
[40]
|
W. Zhu, X.-C. Tai and T. Chan, Augmented Lagrangian method for a mean curvature based image denoising model, Inverse Problems and Imaging, 7 (2013), 1409-1432.
doi: 10.3934/ipi.2013.7.1409.
|