By reviewing the primal-dual hybrid gradient algorithm(PDHG)pro-posed by He,You and Yuan(SIAM J.Image Sci.,7(4)(2014),pp.2526–2537),in this paper we introduce four improved schemes for solving a class of saddle-point...By reviewing the primal-dual hybrid gradient algorithm(PDHG)pro-posed by He,You and Yuan(SIAM J.Image Sci.,7(4)(2014),pp.2526–2537),in this paper we introduce four improved schemes for solving a class of saddle-point problems.Convergence properties of the proposed algorithms are ensured based on weak assumptions,where none of the objective functions are assumed to be strongly convex but the step-sizes in the primal-dual updates are more flexible than the pre-vious.By making use of variational analysis,the global convergence and sublinear convergence rate in the ergodic/nonergodic sense are established,and the numer-ical efficiency of our algorithms is verified by testing an image deblurring problem compared with several existing algorithms.展开更多
Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to...Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.展开更多
基金The work is partly supported by the NSF of China(No.11671318)the NSF of Fujian province(No.2016J01028).
文摘By reviewing the primal-dual hybrid gradient algorithm(PDHG)pro-posed by He,You and Yuan(SIAM J.Image Sci.,7(4)(2014),pp.2526–2537),in this paper we introduce four improved schemes for solving a class of saddle-point problems.Convergence properties of the proposed algorithms are ensured based on weak assumptions,where none of the objective functions are assumed to be strongly convex but the step-sizes in the primal-dual updates are more flexible than the pre-vious.By making use of variational analysis,the global convergence and sublinear convergence rate in the ergodic/nonergodic sense are established,and the numer-ical efficiency of our algorithms is verified by testing an image deblurring problem compared with several existing algorithms.
基金Supported in part by the NNSF of China(11301129,11271323,91330105,11326033)the Zhejiang Provincial Natural Science Foundation of China(LQ13A010025,LZ13A010002)
文摘Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.
