-
Previous Article
A Rellich type theorem for discrete Schrödinger operators
- IPI Home
- This Issue
-
Next Article
Compressive optical deflectometric tomography: A constrained total-variation minimization approach
Retinal vessel segmentation using a finite element based binary level set method
1. | Department of Mathematics and Mechanics, University of Science and Technology Beijing (USTB), Beijing, 100083, China |
2. | Division of Mathematics, University of Dundee, Dundee, DD1 4HN, United Kingdom |
3. | College of Information Science and Engineering, Ocean University of China, Qingdao, 266071, China |
4. | College of Marine Life Science, Ocean University of China, Qingdao, 266071, China |
References:
[1] |
X. Cai, R. Chan, S. Morigi and F. Sgallari, Framelet-based algorithm for segmentation of tubular structures, Lecture Notes in Computer Science, 6667 (2012), 411-422.
doi: 10.1007/978-3-642-24785-9_35. |
[2] |
A. Can, H. Shen, J. N. Turner, H. L. Tanenbaum and B. Roysam, Rapid automated tracing and feature extraction from retinal fundus images using direct exploratory algorithms, IEEE Trans. Inform. Technol. Biomed., 3 (1999), 125-138. |
[3] |
V. Caselles, F. Catte, T. Coll and F. Dibos, A geometric model for active contours in image processing, Numer. Math., 66 (1993), 1-31.
doi: 10.1007/BF01385685. |
[4] |
T. Chan and L. Vese, Active contours without edges, IEEE Image Proc., 10 (2001), 266-277.
doi: 10.1109/83.902291. |
[5] |
S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson and M. Goldbaum, Detection of blood vessel in retinal images using two-dimensional matched filter, IEEE Trans. Med. Imag., 8 (1989), 263-269.
doi: 10.1109/42.34715. |
[6] |
N. Cheung, K. Donaghue, G. Liew, L. Rogers, J. Wang, S. Lim, A. Jenkins, W. Hsu, L. Lee and T. Wong, Quantitative Assessment of Early Diabetic Retinopathy Using Fractal Analysis, Diabetes Care, 32 (2009), 106-110. |
[7] |
J. Chen and A. Amini, Quantifying 3D vascular structures in MRA images using hybrid PDE and geometric deformable models, IEEE Trans. Med. Imag., 10 (2004), 1251-1262. |
[8] |
O. Chutatape, L. Zheng and S. Krishman, Retinal blood vessel detection and tracking by matched Gaussian and Kalman filters, in Proc. IEEE Int. Conf. Eng. Biol. Soc., 6 (1998), 3144-3149.
doi: 10.1109/IEMBS.1998.746160. |
[9] |
B. Dong, A. Chien and Z. Shen, Frame based segmentation for medical images, Commun.Math. Sci., 9 (2011), 551-559.
doi: 10.4310/CMS.2011.v9.n2.a10. |
[10] |
A. F. Frangi, W. J. Niessen, R. M. Hoogeveen, T. van Walsum and M. A. Viergever, Model-based quantitation of 3-D magnetic resonance angiographic images, IEEE Trans. Med. Imag. , 18 (1999), 946-956.
doi: 10.1109/42.811279. |
[11] |
L. Gang, O. Chutatape and S. M. Krishnan, Detection and measurement of retinal vessels in fundus images using amplitude modified second-order Gaussian filter, IEEE. Trans. Biomed. Eng., 49 (2002), 168-172. |
[12] |
R. Glowinski, P. Lin and X. Pan, An operator-splitting method for a liquid crystal model, Comp Phys. Comm., 152 (2003), 242-252.
doi: 10.1016/S0010-4655(02)00823-8. |
[13] |
R. Glowinski, P. Lin and X. Pan, A three-stage operator-splitting/finite element method for the numerical simulation of liquid crystal flow, Int. J. Numer. Anal. Mod., 6 (2009), 440-454. |
[14] |
R. Glowinski and P. Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM, Philadelphia, PA, 1989.
doi: 10.1137/1.9781611970838. |
[15] |
A. Hoover, V. Kouznetsova and M. Goldbaum, Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response, IEEE Trans. Med. Imag., 19 (2000), 203-210. |
[16] |
J. Hua, P. Lin, C. Liu and Q. Wang, Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations, J. Comput. Phys., 230 (2011), 7115-7131.
doi: 10.1016/j.jcp.2011.05.013. |
[17] |
X. Jiang and D. Mojon, Adaptive local thresholding by verification based multithreshold probing with application to vessel detection in retinal images, IEEE Trans. Pattern Anal. Mach. Intell., 25 (2003), 131-137. |
[18] |
M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active contour models, Int. J. Comput. Vis., 1 (1987), 321-331.
doi: 10.1007/BF00133570. |
[19] |
C. Kirbas and F. K. H. Quek, A review of vessel extraction techniques and algorithms, ACM Comput. Surv., 36 (2004), 81-121.
doi: 10.1145/1031120.1031121. |
[20] |
J. Lie, M. Lysaker and X. Tai, A variant of the levelset method and applications to image segmentation, UCLA CAM 03- 50, (2003). |
[21] |
J. Lie, M. Lysaker and X. Tai, A binary level set metod and some application to image processing, UCLA CAM 04-31, (2004). |
[22] |
J. Lie, M. Lysaker and X. Tai, Piecewise constant level set methods and image segmentation. In Scale Space and PDE Methods in Computer Vision, Lectures notes in Computer Sciences, 3459 (2005), 573-584. Springer. |
[23] |
P. Lin and C. Liu, Simulation of singularity dynamics in liquid crystal flows: a C0 finite element approach, J. Comp. Phys., 215 (2006), 348-362.
doi: 10.1016/j.jcp.2005.10.027. |
[24] |
C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-Spectral method, Phys. D, 179 (2003), 211-228.
doi: 10.1016/S0167-2789(03)00030-7. |
[25] |
L. M. Lorigo, O. Faugeras, W. E. L. Grimson, R. Keriven, R. Kikins, A. Nabavi and C.-F. Westin, CURVES: Curve evolution for vessel segmentation, Med. Image. Anal., 5 (2001), 195-206.
doi: 10.1016/S1361-8415(01)00040-8. |
[26] |
C. Lupascu, D. Tegolo and E. Trucco, FABC: Retinal vessel segmentation using adaBoost, IEEE Trans. Inf. Technol. Biomed., 14 (2010), 1267-1274.
doi: 10.1109/TITB.2010.2052282. |
[27] |
T. McInerney and D. Terzopoulos, T-snakes: Topology adaptive snakes, Med. Imag. Anal. , 4 (2000), 73-91.
doi: 10.1016/S1361-8415(00)00008-6. |
[28] |
T. McInerney and D. Terzopoulos, Deformable models in medical image analysis: A survey, Med. Image Anal., 1 (1996), 91-108.
doi: 10.1016/S1361-8415(96)80007-7. |
[29] |
A. M. Mendonca and A. Campilho, Segmentation of Retinal Blood Vessels by Combining the Detection of Centerlines and Morphological Reconstruction, IEEE Trans. Med. Imag., 25 (2006), 1200-1213.
doi: 10.1109/TMI.2006.879955. |
[30] |
C. E. Metz, Basic principles of ROC analysis, Seminars Nucl. Med., 8 (1978), 283-298.
doi: 10.1016/S0001-2998(78)80014-2. |
[31] |
D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math., 42 (1989), 577-685.
doi: 10.1002/cpa.3160420503. |
[32] |
M. Niemeijer, J. Staal, B. Ginneken, M. Long and M. D. Abramoff, Comparative study of retinal vessel segmentation methods on a new publicly available database, Proc. SPIE Med. Imag., 5370 (2004), 648-656.
doi: 10.1117/12.535349. |
[33] |
S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi Formulation, J. Comput. Phys., 79 (1988), 12-49.
doi: 10.1016/0021-9991(88)90002-2. |
[34] |
Q. Sheng, Recent trends in splitting, adaptive and hybrid numerical methods for differential equations, Neural, Parallel and Sci. Comput., 16 (2008), 283-301. |
[35] |
C. Sinthanayothin, J. F. Boyce, T. H. Williamson, H. L. Cook, E. Mensah, S. Lal and D. Usher, Automated detection of diabetic retinopathy on digital fundus images, Diabetic Med., 19 (2002), 105-112.
doi: 10.1046/j.1464-5491.2002.00613.x. |
[36] |
J. Soares, J. Leandro, J. Cesar, H. Jelinek and M. Cree, Retinal vessel segmentation using the 2-d gabor wavelet and supervised classification, IEEE Trans. Med. Imag., 25 (2006), 1214-1222.
doi: 10.1109/TMI.2006.879967. |
[37] |
J. Staal, M. Abramoff, M. Viergever and B. Ginneken, Ridge based vessel segmentation in color images of the retina, IEEE Trans. Med. Imag., 23 (2004), 501-509.
doi: 10.1109/TMI.2004.825627. |
[38] |
K. Sum and P. Cheung, Vessel extraction under non-uniform illumination: A level set approach, IEEE Trans. Biomed. Eng., 55 (2008), 358-360.
doi: 10.1109/TBME.2007.896587. |
[39] |
X. Tai, O. Christiansen, P. Lin and I. Skjaelaaen, A remark on the MBO scheme and some piecewise constant level set methods, Int. J. Comput. Vis., 73 (2007), 61-76. |
[40] |
T. Walter and J. C. Klein, Segmentation of color fundus images of the human retina: Detection of the optic disc and the vascular tree using morphological techniques, in Medical Data Analysis, J. Crespo, V. Maojo, and F. Martin, Eds. Berlin, Germany: Springer-Verlag, 2199 (2001), 282-287. ser. Lecture Notes in Computer Science.
doi: 10.1007/3-540-45497-7_43. |
[41] |
L. Wang, A. Bhalerao and R. Wilson, Analysis of retinal vasculature using a multiresolution hermite model, IEEE Trans. Med. Imag., 26 (2007), 137-152.
doi: 10.1109/TMI.2006.889732. |
[42] |
Y. Wang, G. Ji, P. Lin and E. Trucco, Retinal vessel segmentation using matched filter with multiwavelet kernels and multiscale hierachical decomposition, Pattern Recog., 46 (2013), 2117-2133. |
[43] |
C. Wu and X. Tai, Augmented Lagrangian method, Dual methods and Split-Bregman Iterations for ROF, vectorial TV and higher order models, SIAM J. Imag. Sci., 3 (2010), 300-339.
doi: 10.1137/090767558. |
[44] |
F. Zana and J. C. Klein, Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation, IEEE Trans. Imag. Proc., 10 (2001), 1010-1019.
doi: 10.1109/83.931095. |
[45] |
D. Zonoobi, A. Kassim and W. Shen, Vasculature segmentation in MRA images using gradient compensated geodesic active contours, J. Sign. Process. Syst., 54 (2009), 171-181.
doi: 10.1007/s11265-008-0216-4. |
show all references
References:
[1] |
X. Cai, R. Chan, S. Morigi and F. Sgallari, Framelet-based algorithm for segmentation of tubular structures, Lecture Notes in Computer Science, 6667 (2012), 411-422.
doi: 10.1007/978-3-642-24785-9_35. |
[2] |
A. Can, H. Shen, J. N. Turner, H. L. Tanenbaum and B. Roysam, Rapid automated tracing and feature extraction from retinal fundus images using direct exploratory algorithms, IEEE Trans. Inform. Technol. Biomed., 3 (1999), 125-138. |
[3] |
V. Caselles, F. Catte, T. Coll and F. Dibos, A geometric model for active contours in image processing, Numer. Math., 66 (1993), 1-31.
doi: 10.1007/BF01385685. |
[4] |
T. Chan and L. Vese, Active contours without edges, IEEE Image Proc., 10 (2001), 266-277.
doi: 10.1109/83.902291. |
[5] |
S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson and M. Goldbaum, Detection of blood vessel in retinal images using two-dimensional matched filter, IEEE Trans. Med. Imag., 8 (1989), 263-269.
doi: 10.1109/42.34715. |
[6] |
N. Cheung, K. Donaghue, G. Liew, L. Rogers, J. Wang, S. Lim, A. Jenkins, W. Hsu, L. Lee and T. Wong, Quantitative Assessment of Early Diabetic Retinopathy Using Fractal Analysis, Diabetes Care, 32 (2009), 106-110. |
[7] |
J. Chen and A. Amini, Quantifying 3D vascular structures in MRA images using hybrid PDE and geometric deformable models, IEEE Trans. Med. Imag., 10 (2004), 1251-1262. |
[8] |
O. Chutatape, L. Zheng and S. Krishman, Retinal blood vessel detection and tracking by matched Gaussian and Kalman filters, in Proc. IEEE Int. Conf. Eng. Biol. Soc., 6 (1998), 3144-3149.
doi: 10.1109/IEMBS.1998.746160. |
[9] |
B. Dong, A. Chien and Z. Shen, Frame based segmentation for medical images, Commun.Math. Sci., 9 (2011), 551-559.
doi: 10.4310/CMS.2011.v9.n2.a10. |
[10] |
A. F. Frangi, W. J. Niessen, R. M. Hoogeveen, T. van Walsum and M. A. Viergever, Model-based quantitation of 3-D magnetic resonance angiographic images, IEEE Trans. Med. Imag. , 18 (1999), 946-956.
doi: 10.1109/42.811279. |
[11] |
L. Gang, O. Chutatape and S. M. Krishnan, Detection and measurement of retinal vessels in fundus images using amplitude modified second-order Gaussian filter, IEEE. Trans. Biomed. Eng., 49 (2002), 168-172. |
[12] |
R. Glowinski, P. Lin and X. Pan, An operator-splitting method for a liquid crystal model, Comp Phys. Comm., 152 (2003), 242-252.
doi: 10.1016/S0010-4655(02)00823-8. |
[13] |
R. Glowinski, P. Lin and X. Pan, A three-stage operator-splitting/finite element method for the numerical simulation of liquid crystal flow, Int. J. Numer. Anal. Mod., 6 (2009), 440-454. |
[14] |
R. Glowinski and P. Tallec, Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics, SIAM, Philadelphia, PA, 1989.
doi: 10.1137/1.9781611970838. |
[15] |
A. Hoover, V. Kouznetsova and M. Goldbaum, Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response, IEEE Trans. Med. Imag., 19 (2000), 203-210. |
[16] |
J. Hua, P. Lin, C. Liu and Q. Wang, Energy law preserving C0 finite element schemes for phase field models in two-phase flow computations, J. Comput. Phys., 230 (2011), 7115-7131.
doi: 10.1016/j.jcp.2011.05.013. |
[17] |
X. Jiang and D. Mojon, Adaptive local thresholding by verification based multithreshold probing with application to vessel detection in retinal images, IEEE Trans. Pattern Anal. Mach. Intell., 25 (2003), 131-137. |
[18] |
M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active contour models, Int. J. Comput. Vis., 1 (1987), 321-331.
doi: 10.1007/BF00133570. |
[19] |
C. Kirbas and F. K. H. Quek, A review of vessel extraction techniques and algorithms, ACM Comput. Surv., 36 (2004), 81-121.
doi: 10.1145/1031120.1031121. |
[20] |
J. Lie, M. Lysaker and X. Tai, A variant of the levelset method and applications to image segmentation, UCLA CAM 03- 50, (2003). |
[21] |
J. Lie, M. Lysaker and X. Tai, A binary level set metod and some application to image processing, UCLA CAM 04-31, (2004). |
[22] |
J. Lie, M. Lysaker and X. Tai, Piecewise constant level set methods and image segmentation. In Scale Space and PDE Methods in Computer Vision, Lectures notes in Computer Sciences, 3459 (2005), 573-584. Springer. |
[23] |
P. Lin and C. Liu, Simulation of singularity dynamics in liquid crystal flows: a C0 finite element approach, J. Comp. Phys., 215 (2006), 348-362.
doi: 10.1016/j.jcp.2005.10.027. |
[24] |
C. Liu and J. Shen, A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-Spectral method, Phys. D, 179 (2003), 211-228.
doi: 10.1016/S0167-2789(03)00030-7. |
[25] |
L. M. Lorigo, O. Faugeras, W. E. L. Grimson, R. Keriven, R. Kikins, A. Nabavi and C.-F. Westin, CURVES: Curve evolution for vessel segmentation, Med. Image. Anal., 5 (2001), 195-206.
doi: 10.1016/S1361-8415(01)00040-8. |
[26] |
C. Lupascu, D. Tegolo and E. Trucco, FABC: Retinal vessel segmentation using adaBoost, IEEE Trans. Inf. Technol. Biomed., 14 (2010), 1267-1274.
doi: 10.1109/TITB.2010.2052282. |
[27] |
T. McInerney and D. Terzopoulos, T-snakes: Topology adaptive snakes, Med. Imag. Anal. , 4 (2000), 73-91.
doi: 10.1016/S1361-8415(00)00008-6. |
[28] |
T. McInerney and D. Terzopoulos, Deformable models in medical image analysis: A survey, Med. Image Anal., 1 (1996), 91-108.
doi: 10.1016/S1361-8415(96)80007-7. |
[29] |
A. M. Mendonca and A. Campilho, Segmentation of Retinal Blood Vessels by Combining the Detection of Centerlines and Morphological Reconstruction, IEEE Trans. Med. Imag., 25 (2006), 1200-1213.
doi: 10.1109/TMI.2006.879955. |
[30] |
C. E. Metz, Basic principles of ROC analysis, Seminars Nucl. Med., 8 (1978), 283-298.
doi: 10.1016/S0001-2998(78)80014-2. |
[31] |
D. Mumford and J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Commun. Pure Appl. Math., 42 (1989), 577-685.
doi: 10.1002/cpa.3160420503. |
[32] |
M. Niemeijer, J. Staal, B. Ginneken, M. Long and M. D. Abramoff, Comparative study of retinal vessel segmentation methods on a new publicly available database, Proc. SPIE Med. Imag., 5370 (2004), 648-656.
doi: 10.1117/12.535349. |
[33] |
S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi Formulation, J. Comput. Phys., 79 (1988), 12-49.
doi: 10.1016/0021-9991(88)90002-2. |
[34] |
Q. Sheng, Recent trends in splitting, adaptive and hybrid numerical methods for differential equations, Neural, Parallel and Sci. Comput., 16 (2008), 283-301. |
[35] |
C. Sinthanayothin, J. F. Boyce, T. H. Williamson, H. L. Cook, E. Mensah, S. Lal and D. Usher, Automated detection of diabetic retinopathy on digital fundus images, Diabetic Med., 19 (2002), 105-112.
doi: 10.1046/j.1464-5491.2002.00613.x. |
[36] |
J. Soares, J. Leandro, J. Cesar, H. Jelinek and M. Cree, Retinal vessel segmentation using the 2-d gabor wavelet and supervised classification, IEEE Trans. Med. Imag., 25 (2006), 1214-1222.
doi: 10.1109/TMI.2006.879967. |
[37] |
J. Staal, M. Abramoff, M. Viergever and B. Ginneken, Ridge based vessel segmentation in color images of the retina, IEEE Trans. Med. Imag., 23 (2004), 501-509.
doi: 10.1109/TMI.2004.825627. |
[38] |
K. Sum and P. Cheung, Vessel extraction under non-uniform illumination: A level set approach, IEEE Trans. Biomed. Eng., 55 (2008), 358-360.
doi: 10.1109/TBME.2007.896587. |
[39] |
X. Tai, O. Christiansen, P. Lin and I. Skjaelaaen, A remark on the MBO scheme and some piecewise constant level set methods, Int. J. Comput. Vis., 73 (2007), 61-76. |
[40] |
T. Walter and J. C. Klein, Segmentation of color fundus images of the human retina: Detection of the optic disc and the vascular tree using morphological techniques, in Medical Data Analysis, J. Crespo, V. Maojo, and F. Martin, Eds. Berlin, Germany: Springer-Verlag, 2199 (2001), 282-287. ser. Lecture Notes in Computer Science.
doi: 10.1007/3-540-45497-7_43. |
[41] |
L. Wang, A. Bhalerao and R. Wilson, Analysis of retinal vasculature using a multiresolution hermite model, IEEE Trans. Med. Imag., 26 (2007), 137-152.
doi: 10.1109/TMI.2006.889732. |
[42] |
Y. Wang, G. Ji, P. Lin and E. Trucco, Retinal vessel segmentation using matched filter with multiwavelet kernels and multiscale hierachical decomposition, Pattern Recog., 46 (2013), 2117-2133. |
[43] |
C. Wu and X. Tai, Augmented Lagrangian method, Dual methods and Split-Bregman Iterations for ROF, vectorial TV and higher order models, SIAM J. Imag. Sci., 3 (2010), 300-339.
doi: 10.1137/090767558. |
[44] |
F. Zana and J. C. Klein, Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation, IEEE Trans. Imag. Proc., 10 (2001), 1010-1019.
doi: 10.1109/83.931095. |
[45] |
D. Zonoobi, A. Kassim and W. Shen, Vasculature segmentation in MRA images using gradient compensated geodesic active contours, J. Sign. Process. Syst., 54 (2009), 171-181.
doi: 10.1007/s11265-008-0216-4. |
[1] |
Liejune Shiau, Roland Glowinski. Operator splitting method for friction constrained dynamical systems. Conference Publications, 2005, 2005 (Special) : 806-815. doi: 10.3934/proc.2005.2005.806 |
[2] |
Esther Klann, Ronny Ramlau, Wolfgang Ring. A Mumford-Shah level-set approach for the inversion and segmentation of SPECT/CT data. Inverse Problems and Imaging, 2011, 5 (1) : 137-166. doi: 10.3934/ipi.2011.5.137 |
[3] |
Zhili Ge, Gang Qian, Deren Han. Global convergence of an inexact operator splitting method for monotone variational inequalities. Journal of Industrial and Management Optimization, 2011, 7 (4) : 1013-1026. doi: 10.3934/jimo.2011.7.1013 |
[4] |
Lijian Jiang, Craig C. Douglas. Analysis of an operator splitting method in 4D-Var. Conference Publications, 2009, 2009 (Special) : 394-403. doi: 10.3934/proc.2009.2009.394 |
[5] |
Berat Karaagac. Numerical treatment of Gray-Scott model with operator splitting method. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2373-2386. doi: 10.3934/dcdss.2020143 |
[6] |
Jiangfeng Huang, Zhiliang Deng, Liwei Xu. A Bayesian level set method for an inverse medium scattering problem in acoustics. Inverse Problems and Imaging, 2021, 15 (5) : 1077-1097. doi: 10.3934/ipi.2021029 |
[7] |
Kangkang Deng, Zheng Peng, Jianli Chen. Sparse probabilistic Boolean network problems: A partial proximal-type operator splitting method. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1881-1896. doi: 10.3934/jimo.2018127 |
[8] |
Peter Frolkovič, Viera Kleinová. A new numerical method for level set motion in normal direction used in optical flow estimation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 851-863. doi: 10.3934/dcdss.2020347 |
[9] |
Wangtao Lu, Shingyu Leung, Jianliang Qian. An improved fast local level set method for three-dimensional inverse gravimetry. Inverse Problems and Imaging, 2015, 9 (2) : 479-509. doi: 10.3934/ipi.2015.9.479 |
[10] |
Yunmei Chen, Xianqi Li, Yuyuan Ouyang, Eduardo Pasiliao. Accelerated bregman operator splitting with backtracking. Inverse Problems and Imaging, 2017, 11 (6) : 1047-1070. doi: 10.3934/ipi.2017048 |
[11] |
Ye Yuan, Yan Ren, Xiaodong Liu, Jing Wang. Approach to image segmentation based on interval neutrosophic set. Numerical Algebra, Control and Optimization, 2020, 10 (1) : 1-11. doi: 10.3934/naco.2019028 |
[12] |
Denis Dmitriev, Jonathan Jedwab. Bounds on the growth rate of the peak sidelobe level of binary sequences. Advances in Mathematics of Communications, 2007, 1 (4) : 461-475. doi: 10.3934/amc.2007.1.461 |
[13] |
Leyu Hu, Wenxing Zhang, Xingju Cai, Deren Han. A parallel operator splitting algorithm for solving constrained total-variation retinex. Inverse Problems and Imaging, 2020, 14 (6) : 1135-1156. doi: 10.3934/ipi.2020058 |
[14] |
Manh Hong Duong, Yulong Lu. An operator splitting scheme for the fractional kinetic Fokker-Planck equation. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5707-5727. doi: 10.3934/dcds.2019250 |
[15] |
Bin Dong, Aichi Chien, Yu Mao, Jian Ye, Fernando Vinuela, Stanley Osher. Level set based brain aneurysm capturing in 3D. Inverse Problems and Imaging, 2010, 4 (2) : 241-255. doi: 10.3934/ipi.2010.4.241 |
[16] |
Ji-Woong Jang, Young-Sik Kim, Sang-Hyo Kim. New design of quaternary LCZ and ZCZ sequence set from binary LCZ and ZCZ sequence set. Advances in Mathematics of Communications, 2009, 3 (2) : 115-124. doi: 10.3934/amc.2009.3.115 |
[17] |
Xiaohui Liu, Jinhua Wang, Dianhua Wu. Two new classes of binary sequence pairs with three-level cross-correlation. Advances in Mathematics of Communications, 2015, 9 (1) : 117-128. doi: 10.3934/amc.2015.9.117 |
[18] |
Petra Csomós, Hermann Mena. Fourier-splitting method for solving hyperbolic LQR problems. Numerical Algebra, Control and Optimization, 2018, 8 (1) : 17-46. doi: 10.3934/naco.2018002 |
[19] |
Kai Wang, Lingling Xu, Deren Han. A new parallel splitting descent method for structured variational inequalities. Journal of Industrial and Management Optimization, 2014, 10 (2) : 461-476. doi: 10.3934/jimo.2014.10.461 |
[20] |
Hao Chen, Kaitai Li, Yuchuan Chu, Zhiqiang Chen, Yiren Yang. A dimension splitting and characteristic projection method for three-dimensional incompressible flow. Discrete and Continuous Dynamical Systems - B, 2019, 24 (1) : 127-147. doi: 10.3934/dcdsb.2018111 |
2020 Impact Factor: 1.639
Tools
Metrics
Other articles
by authors
[Back to Top]