Two-phase image segmentation is a fundamental task to partition an image into foreground and background.In this paper,two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segment...Two-phase image segmentation is a fundamental task to partition an image into foreground and background.In this paper,two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation.They extend the convex regularization on the characteristic function on the image domain to the nonconvex case,which are able to better obtain piecewise constant regions with neat boundaries.By analyzing the proposed non-Lipschitz model,we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm.This leads to two alternating strongly convex subproblems which can be easily solved.Similarly,we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case.Using the Kurdyka-Lojasiewicz property of the objective function,we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem.Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.展开更多
The era of big data in healthcare is here, and this era will significantly improve medicine and especially oncology. However, traditional machine learning algorithms need to be promoted to solve such large-scale real-...The era of big data in healthcare is here, and this era will significantly improve medicine and especially oncology. However, traditional machine learning algorithms need to be promoted to solve such large-scale real-world problems due to a large amount of data that needs to be analyzed and the difficulty in solving problems with nonconvex nonlinear settings. We aim to minimize the composite of a smooth nonlinear function and a block-separable nonconvex function on a large number of block variables with inequality constraints. We propose a novel parallel first-order optimization method, called asynchronous block coordinate descent with time perturbation (ATP), which adopts a time perturbation technique that escapes from saddle points and sub-optimal local points. The details of the proposed method are presented with analyses of convergence and iteration complexity properties. Experiments conducted on real-world machine learning problems validate the efficacy of our proposed method. The experimental results demonstrate that time perturbation enables ATP to escape from saddle points and sub-optimal points, providing a promising way to handle nonconvex optimization problems with inequality constraints employing asynchronous block coordinate descent. The asynchronous parallel implementation on shared memory multi-core platforms indicates that the proposed algorithm, ATP, has strong scalability.展开更多
针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化...针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化处理,并在x-子问题中引入惯性效应。在适当的假设条件下,建立了算法的全局收敛性;同时引入满足Kurdyka-Lojasiewicz不等式的辅助函数,验证了算法的强收敛性。通过两个数值实验表明,引入惯性效应的算法比没有惯性效应的算法收敛性能更好。展开更多
Synthetic aperture radar(SAR) image despeckling has been an attractive problem in remote sensing.The main challenge is to suppress speckle while preserving edges and preventing unnatural artifacts(such as annoying art...Synthetic aperture radar(SAR) image despeckling has been an attractive problem in remote sensing.The main challenge is to suppress speckle while preserving edges and preventing unnatural artifacts(such as annoying artifacts in homogeneous regions and over-smoothed edges).To address these problems,this paper proposes a new variational model with a nonconvex nonsmooth Lp(0 <p<1) norm regularization.It incorporates Lp(0<p<1) norm regularization and I-divergence fidelity term.Due to the nonconvex nonsmooth property,the regularization can better recover neat edges and homogeneous regions.The Ⅰ-divergence fidelity term is used to suppress the multiplicative noise effectively.Moreover,based on variable-splitting and alternating direction method of multipliers(ADMM) method,an efficient algorithm is proposed for solving this model.Intensive experimental results demonstrate that nonconvex nonsmooth model is superior to other state-of-the-art approaches qualitatively and quantitatively.展开更多
In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their al...In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance.Moreover,the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an(afne-scaled)Clarke stationary point of the original nonsmooth and nonconvex problem.Their experimental results indicate the effectiveness of the proposed algorithm.展开更多
基金supported by the National Natural Science Foundation of China(NSFC)(No.12001144)Zhejiang Provincial Natural Science Foundation of China(No.LQ20A010007)+1 种基金Chern Institute of Mathematicssupported by the National Natural Science Foundation of China(NSFC)(Nos.11871035,11531013).
文摘Two-phase image segmentation is a fundamental task to partition an image into foreground and background.In this paper,two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation.They extend the convex regularization on the characteristic function on the image domain to the nonconvex case,which are able to better obtain piecewise constant regions with neat boundaries.By analyzing the proposed non-Lipschitz model,we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm.This leads to two alternating strongly convex subproblems which can be easily solved.Similarly,we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case.Using the Kurdyka-Lojasiewicz property of the objective function,we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem.Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.
基金Project supported by the National Key R&D Program of China(No.2018YFB2101100)the National Natural Science Foundation of China(Nos.61806216 and 61702533)。
文摘The era of big data in healthcare is here, and this era will significantly improve medicine and especially oncology. However, traditional machine learning algorithms need to be promoted to solve such large-scale real-world problems due to a large amount of data that needs to be analyzed and the difficulty in solving problems with nonconvex nonlinear settings. We aim to minimize the composite of a smooth nonlinear function and a block-separable nonconvex function on a large number of block variables with inequality constraints. We propose a novel parallel first-order optimization method, called asynchronous block coordinate descent with time perturbation (ATP), which adopts a time perturbation technique that escapes from saddle points and sub-optimal local points. The details of the proposed method are presented with analyses of convergence and iteration complexity properties. Experiments conducted on real-world machine learning problems validate the efficacy of our proposed method. The experimental results demonstrate that time perturbation enables ATP to escape from saddle points and sub-optimal points, providing a promising way to handle nonconvex optimization problems with inequality constraints employing asynchronous block coordinate descent. The asynchronous parallel implementation on shared memory multi-core platforms indicates that the proposed algorithm, ATP, has strong scalability.
文摘针对目标函数中包含耦合函数H(x,y)的非凸非光滑极小化问题,提出了一种线性惯性交替乘子方向法(Linear Inertial Alternating Direction Method of Multipliers,LIADMM)。为了方便子问题的求解,对目标函数中的耦合函数H(x,y)进行线性化处理,并在x-子问题中引入惯性效应。在适当的假设条件下,建立了算法的全局收敛性;同时引入满足Kurdyka-Lojasiewicz不等式的辅助函数,验证了算法的强收敛性。通过两个数值实验表明,引入惯性效应的算法比没有惯性效应的算法收敛性能更好。
基金The Major State Basic Research Development Program(2011CB302903)the China Postdoctoral Science Foundation(20100481167)+2 种基金the National Natural Science Foundation of China(60971129)the Natural Science Foundation of Jiangsu Province(BK2011793)the Postdoctoral Science Foundation of Jiangsu Province(1101022B)
基金Supported by the National Natural Science Foundation of China(No.41971356,41701446)the National Key Research and Development Program of China(No.2018YFB0505500)the Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation,Ministry of Natural Resources(No.KF-2020-05-011)。
文摘Synthetic aperture radar(SAR) image despeckling has been an attractive problem in remote sensing.The main challenge is to suppress speckle while preserving edges and preventing unnatural artifacts(such as annoying artifacts in homogeneous regions and over-smoothed edges).To address these problems,this paper proposes a new variational model with a nonconvex nonsmooth Lp(0 <p<1) norm regularization.It incorporates Lp(0<p<1) norm regularization and I-divergence fidelity term.Due to the nonconvex nonsmooth property,the regularization can better recover neat edges and homogeneous regions.The Ⅰ-divergence fidelity term is used to suppress the multiplicative noise effectively.Moreover,based on variable-splitting and alternating direction method of multipliers(ADMM) method,an efficient algorithm is proposed for solving this model.Intensive experimental results demonstrate that nonconvex nonsmooth model is superior to other state-of-the-art approaches qualitatively and quantitatively.
基金supported by the National Natural Science Foundation of China(No.12001144)Zhejiang Provincial Natural Science Foundation of China(No.LQ20A010007)NSF/DMS-2152961。
文摘In this paper,the authors propose a novel smoothing descent type algorithm with extrapolation for solving a class of constrained nonsmooth and nonconvex problems,where the nonconvex term is possibly nonsmooth.Their algorithm adopts the proximal gradient algorithm with extrapolation and a safe-guarding policy to minimize the smoothed objective function for better practical and theoretical performance.Moreover,the algorithm uses a easily checking rule to update the smoothing parameter to ensure that any accumulation point of the generated sequence is an(afne-scaled)Clarke stationary point of the original nonsmooth and nonconvex problem.Their experimental results indicate the effectiveness of the proposed algorithm.
