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
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
In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both cons...In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.展开更多
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(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supported by the Zhejiang Provincial Natural Science Foundation of China under grant No.LQ21A010003.
文摘In this paper,we offer a new sparse recovery strategy based on the generalized error function.The introduced penalty function involves both the shape and the scale parameters,making it extremely flexible.For both constrained and unconstrained models,the theoretical analysis results in terms of the null space property,the spherical section property and the restricted invertibility factor are established.The practical algorithms via both the iteratively reweighted■_(1)and the difference of convex functions algorithms are presented.Numerical experiments are carried out to demonstrate the benefits of the suggested approach in a variety of circumstances.Its practical application in magnetic resonance imaging(MRI)reconstruction is also investigated.
