This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order a...This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function.Under a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence properties.We also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method.展开更多
In[3],Chan and Wong proposed to use total variational regularization for both images and point spread functions in blind deconvolution.Their experimental results show that the detail of the restored images cannot be r...In[3],Chan and Wong proposed to use total variational regularization for both images and point spread functions in blind deconvolution.Their experimental results show that the detail of the restored images cannot be recovered.In this paper,we consider images in Lipschitz spaces,and propose to use Lipschitz regularization for images and total variational regularization for point spread functions in blind deconvolution.Our experimental results show that such combination of Lipschitz and total variational regularization methods can recover both images and point spread functions quite well.展开更多
We study iterative methods for solving a set of sparse non-negative tensor equations （multivariate polynomial systems） arising from data mining applications such as information retrieval by query search and communit...We study iterative methods for solving a set of sparse non-negative tensor equations （multivariate polynomial systems） arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.展开更多
In this paper, we study two variational blind deblurring models for a single linage,The first model is to use the total variation prior in both image and blur, while the second model is to use the flame based prior in...In this paper, we study two variational blind deblurring models for a single linage,The first model is to use the total variation prior in both image and blur, while the second model is to use the flame based prior in both image and blur. The main contribution of this paper is to show how to employ the generalized cross validation （GCV） method efficiently and automatically to estimate the two regularization parameters associated with the priors in these two blind motion deblurring models. Our experimental results show that the visual quality of restored images by the proposed method is very good, and they are competitive with the tested existing methods. We will also demonstrate the proposed method is also very efficient.展开更多
In this paper,we propose a multiphase fuzzy region competition model for texture image segmentation.In the functional,each region is represented by a fuzzy membership function and a probability density function that i...In this paper,we propose a multiphase fuzzy region competition model for texture image segmentation.In the functional,each region is represented by a fuzzy membership function and a probability density function that is estimated by a nonparametric kernel density estimation.The overall algorithm is very efficient as both the fuzzy membership function and the probability density function can be implemented easily.We apply the proposed method to synthetic and natural texture images,and synthetic aperture radar images.Our experimental results have shown that the proposed method is competitive with the other state-of-the-art segmentation methods.展开更多
We present a multi-phase image segmentation method based on the histogram of the Gabor feature space,which consists of a set of Gabor-filter responses with various orientations,scales and frequencies.Our model replace...We present a multi-phase image segmentation method based on the histogram of the Gabor feature space,which consists of a set of Gabor-filter responses with various orientations,scales and frequencies.Our model replaces the error function term in the original fuzzy region competition model with squared 2-Wasserstein distance function,which is a metric to measure the distance of two histograms.The energy functional is minimized by alternative minimization method and the existence of closed-form solutions is guaranteed when the exponent of the fuzzy membership term being 1 or 2.We test our model on both simple synthetic texture images and complex natural images with two or more phases.Experimental results are shown and compared to other recent results.展开更多
基金supported by NSFC Grant 10601043,NCETXMUSRF for ROCS,SEM+2 种基金supported by RGC 201508HKBU FRGssupported by the Hong Kong Research Grant Council
文摘This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function.We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function.Under a local Lipschitzian error bound assumption,we show that the algorithm possesses global and local linear convergence properties.We also give some numerical tests(including image recovery examples) to illustrate the efficiency of the proposed method.
基金This research is supported in part by RGC 7046/03P,7035/04P,7035/05P and HKBU FRGs.
文摘In[3],Chan and Wong proposed to use total variational regularization for both images and point spread functions in blind deconvolution.Their experimental results show that the detail of the restored images cannot be recovered.In this paper,we consider images in Lipschitz spaces,and propose to use Lipschitz regularization for images and total variational regularization for point spread functions in blind deconvolution.Our experimental results show that such combination of Lipschitz and total variational regularization methods can recover both images and point spread functions quite well.
文摘We study iterative methods for solving a set of sparse non-negative tensor equations （multivariate polynomial systems） arising from data mining applications such as information retrieval by query search and community discovery in multi-dimensional networks. By making use of sparse and non-negative tensor structure, we develop Jacobi and Gauss-Seidel methods for solving tensor equations. The multiplication of tensors with vectors are required at each iteration of these iterative methods, the cost per iteration depends on the number of non-zeros in the sparse tensors. We show linear convergence of the Jacobi and Gauss-Seidel methods under suitable conditions, and therefore, the set of sparse non-negative tensor equations can be solved very efficiently. Experimental results on information retrieval by query search and community discovery in multi-dimensional networks are presented to illustrate the application of tensor equations and the effectiveness of the proposed methods.
文摘In this paper, we study two variational blind deblurring models for a single linage,The first model is to use the total variation prior in both image and blur, while the second model is to use the flame based prior in both image and blur. The main contribution of this paper is to show how to employ the generalized cross validation （GCV） method efficiently and automatically to estimate the two regularization parameters associated with the priors in these two blind motion deblurring models. Our experimental results show that the visual quality of restored images by the proposed method is very good, and they are competitive with the tested existing methods. We will also demonstrate the proposed method is also very efficient.
基金supported partially by RGC 201508,HKBU FRGsThe Research Fund for the Doctoral Program of Higher Education(200802691037)the Natural Science Foundation of Shanghai(10ZR1410200).
文摘In this paper,we propose a multiphase fuzzy region competition model for texture image segmentation.In the functional,each region is represented by a fuzzy membership function and a probability density function that is estimated by a nonparametric kernel density estimation.The overall algorithm is very efficient as both the fuzzy membership function and the probability density function can be implemented easily.We apply the proposed method to synthetic and natural texture images,and synthetic aperture radar images.Our experimental results have shown that the proposed method is competitive with the other state-of-the-art segmentation methods.
文摘We present a multi-phase image segmentation method based on the histogram of the Gabor feature space,which consists of a set of Gabor-filter responses with various orientations,scales and frequencies.Our model replaces the error function term in the original fuzzy region competition model with squared 2-Wasserstein distance function,which is a metric to measure the distance of two histograms.The energy functional is minimized by alternative minimization method and the existence of closed-form solutions is guaranteed when the exponent of the fuzzy membership term being 1 or 2.We test our model on both simple synthetic texture images and complex natural images with two or more phases.Experimental results are shown and compared to other recent results.
