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A new trust region algorithm for image restoration

Science China Mathematics 2005年第2期48卷 169-184页

作者： WEN Zaiwen & WANG Yanfei State key laboratory of scientific engineering computing, Institute of Computational Mathematics and scientific/engineering computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China National key laboratory on Remote Sensing Science, Institute of Remote Sensing Applications, Chinese Academy of Sciences, Beijing 100101, China 1. State Key Laboratory of Scientific Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. National Key Laboratory on Remote Sensing Science Institute of Remote Sensing Applications Chinese Academy of Sciences 100101 Beijing China

The image restoration problems play an important role in remote sensing and astronomical image analysis. One common method for the recovery of a true image from corrupted or blurred image is the least squares error (LSE) method. But the LSE method is unstable in practical applications. A popular way to overcome instability is the Tikhonov regularization. However, difficulties will encounter when adjusting the so-called regularization parameter a. Moreover, how to truncate the iteration at appropriate steps is also challenging. In this paper we use the trust region method to deal with the image restoration problem, meanwhile, the trust region subproblem is solved by the truncated Lanczos method and the preconditioned truncated Lanczos method. We also develop a fast algorithm for evaluating the Kronecker matrix-vector product when the matrix is banded. The trust region method is very stable and robust, and it has the nice property of updating the trust region automatically. This releases us from tedious finding the regularization parameters and truncation levels. Some numerical tests on remotely sensed images are given to show that the trust region method is promising.

关键词： trust region algorithm, image restoration, Lanczos method, Kronecker matrix-vector product, preconditioning.

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Infinitely Many Symmetries of Konopelchenko-Dubrovsky Equation

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Communications in Theoretical Physics 2005年第3X期44卷 385-388页

作者： LI Zhi-Fang RUAN Hang-Yu Department of Physics Ningbo University Ningbo 315211 China Nonlinear Science Center and Physics Department of Ningbo University Ningbo 315211 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences the Chinese Academy of Sciences P.O. Box 2719 Beijing 100080 China

A set of generalized symmetries with arbitrary functions of t for the Konopelchenko-Dubrovsky (KD)equation in 2+1 space dimensions is given by using a direct method called formal function series method presented by Lo... 详细信息

关键词： formal function series method Konopelchenko-Dubrovsky equation infinite dimensional generalized ω∞ algebra

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An improved spatio-temporal video error concealment algorithm using partial differential equation

An improved spatio-temporal video error concealment algorith...

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Multimedia Systems and Applications VIII

作者： Hu, Yang Chen, Yan Li, Houqiang MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of Electrical Engineering and Information Science University of Science and Technology of China Hefei 230027

ISBN: (纸本)0819460397

The application of error concealment in video communication is very important when compressed video sequences are transmitted over error-prone networks and erroneously received. In this paper, we propose a novel error concealment scheme, in which the concealment problem is formulated as minimizing, in a weighted manner, the difference between the gradient of the reconstructed data and a prescribed vector field under given boundary condition. Instead of using the motion compensated block as the final recovered pixel values, we use the gradient of the motion compensated block together with the surrounding correctly decoded pixels of the damaged block to reconstruct the lost data. Both temporal and spatial correlations of the video signals are exploited in the proposed scheme. A well designed weighting factor is used to control the regulation level at a desired direction according to the local blockiness degree at the boundaries of the recovered block. The experimental results show that the proposed algorithm is able to achieve higher PSNR as well as better visual quality in comparison with the error concealment feature implemented in the H.264 reference software. The blocking effects are greatly alleviated while the structural information in the interior of the recovered block is well preserved.

关键词： Algorithmic languages

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Graph embedding: A general framework for dimensionality reduction

Graph embedding: A general framework for dimensionality redu...

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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005

作者： Yan, Shuicheng Xu, Dong Zhang, Benyu Zhang, Hong-Jiang Department of Information Engineering Chinese University of Hong Kong Shatin Hong Kong MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Microsoft Research Asia Beijing China

ISBN: (纸本)769523722

In the last decades, a large family of algorithms - supervised or unsupervised;stemming from statistic or geometry theory - have been proposed to provide different solutions to the problem of dimensionality reduction. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and kernelization, which in theory reveals the underlying objective shared by most previous algorithms. It presents a unified perspective to understand these algorithms; that is, each algorithm can be considered as the direct graph embedding or its linear/kernel extension of some specific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimensionality reduction. To this end, we propose a new supervised algorithm, Marginal Fisher Analysis (MFA), for dimensionality reduction by designing two graphs that characterize the intra-class compactness and inter-class separability, respectively. MFA measures the intra-class compactness with the distance between each data point and its neighboring points of the same class, and measures the inter-class separability with the class margins; thus it overcomes the limitations of traditional Linear Discriminant Analysis algorithm in terms of data distribution assumptions and available projection directions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA. © 2005 IEEE.

关键词： Embedded systems

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Concurrent subspaces analysis

Concurrent subspaces analysis

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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005

作者： Xu, Dong Yan, Shuicheng Zhang, Lei Zhang, Hong-Jiang Liu, Zhengkai Shum, Heung-Yeung MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Department of Information Engineering Chinese University of Hong Kong Shatin Hong Kong Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

A representative subspace is significant for image analysis, while the corresponding techniques often suffer from the curse of dimensionality dilemma. In this paper, we propose a new algorithm, called Concurrent Subspaces Analysis (CSA), to derive representative subspaces by encoding image objects as 2 nd or even higher order tensors. In CSA, an original higher dimensional tensor is transformed into a lower dimensional one using multiple concurrent subspaces that characterize the most representative information of different dimensions, respectively. Moreover, an efficient procedure is provided to learn these subspaces in an iterative manner. As analyzed in this paper, each sub-step of CSA takes the column vectors of the matrices, which are acquired from the k-mode unfolding of the tensors, as the new objects to be analyzed, thus the curse of dimensionality dilemma can be effectively avoided. The extensive experiments on the 3rd order tensor data, simulated video sequences and Gabor filtered digital number image database show that CSA outper-forms Principal Component Analysis in terms of both reconstruction and classification capability. © 2005 IEEE.

关键词： Image analysis

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Fisher+Kernel Criterion for discriminant analysis

Fisher+Kernel Criterion for discriminant analysis

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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005

作者： Yang, Shu Yan, Shuicheng Xu, Dong Tang, Xiaoou Zhang, Chao National Laboratory on Machine Perception Peking University Beijing China Department of Information Engineering Chinese University of Hong Kong Shatin Hong Kong MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Microsoft Research Asia Beijing China

ISBN: (纸本)769523722

We simultaneously approach two tasks of nonlinear discriminant analysis and kernel selection problem by proposing a unified criterion, Fisher+Kernel Criterion. In addition, an efficient procedure is derived to optimize this new criterion in an iterative manner. More specifically, original input vector is first transformed into a higher dimensional feature matrix through a battery of nonlinear mappings involved in different kernels. Then, based on the feature matrices, FKC is presented within two coupled projection spaces: one projection space is used to search for the optimal combinations of kernels; while the other encodes the optimal nonlinear discriminating projection directions. Our proposed method is a unified framework for both kernel selection and nonlinear discriminant analysis. Besides, the algorithm potentially alleviates overfitting problem existing in traditional KDA and has no singularity problems in most cases. The effectiveness of our proposed algorithm is validated by extensive face recognition experiments on several datasets. © 2005 IEEE.

关键词： Pattern recognition

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A Discrete Scheme of Laplace-Beltrami Operator and Its Convergence over Quadrilateral Meshes

A Discrete Scheme of Laplace-Beltrami Operator and Its Conve...

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第二届全国几何设计与计算学术会议

作者： Dan Liu Guoliang Xu State Key Laboratory of Scientific and Engineering Computing Institute of Computational MathematicsAcademy of Mathematics and System SciencesChinese Academy of Sciences

Laplace-Beltrami operator and its discretization play a central role in several applications in the fields of computer graphics and computer aided geometric *** this paper,a discrete scheme for Laplace-Beltrami operator over quadrilateral meshes is constructed based on a bilinear interpolation of the quadrilateral. Convergence results for the proposed discrete scheme are established under some conditions.

关键词： Laplace-Beltrami Operator Quadrilateral meshes Discretization Convergence

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Discriminant analysis with tensor representation

Discriminant analysis with tensor representation

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2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2005

作者： Yan, Shuicheng Xu, Dong Yang, Qiang Zhang, Lei Tang, Xiaoou Zhang, Hong-Jiang Department of Information Engineering Chinese University of Hong Kong Shatin Hong Kong MOE-Microsoft Key Laboratory of Multimedia Computing and Communication Department of EEIS University of Science and Technology of China Hefei Anhui China Department of Computer Science Hong Kong University of Science and Technology Hong Kong Hong Kong Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

In this paper, we present a novel approach to solving the supervised dimensionality reduction problem by encoding an image object as a general tensor of 2nd or higher order. First, we propose a Discriminant Tensor Criterion (DTC), whereby multiple interrelated lower-dimensional discriminative subspaces are derived for feature selection. Then, a novel approach called k-mode Cluster-based Discriminant Analysis is presented to iteratively learn these subspaces by unfolding the tensor along different tensor dimensions. We call this algorithm Discriminant Analysis with Tensor Representation (DATER), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes;2) for classification problems involving higher-order tensors, the DATER algorithm can avoid the curse of dimensionality dilemma and overcome the small sample size problem;and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in generalized eigenvalue decomposition. We provide extensive experiments by encoding face images as 2nd or 3rd order tensors to demonstrate that the proposed DATER algorithm based on higher order tensors has the potential to outperform the traditional subspace learning algorithms, especially in the small sample size cases. © 2005 IEEE.

关键词： Problem solving

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Graph embedding: a general framework for dimensionality reduction

Graph embedding: a general framework for dimensionality redu...

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Shuicheng Yan Dong Xu Benyu Zhang Hong-Jiang Zhang Department of Information Engineering Chinese University of Hong Kong Sha Tin Hong Kong China MOE-Microsoft Key Laboratory of Multimedia Computing and Communication & Department of EEIS University of Science and Technology Hefei Anhui China Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

In the last decades, a large family of algorithms - supervised or unsupervised; stemming from statistic or geometry theory - have been proposed to provide different solutions to the problem of dimensionality reduction. In this paper, beyond the different motivations of these algorithms, we propose a general framework, graph embedding along with its linearization and kernelization, which in theory reveals the underlying objective shared by most previous algorithms. It presents a unified perspective to understand these algorithms; that is, each algorithm can be considered as the direct graph embedding or its linear/kernel extension of some specific graph characterizing certain statistic or geometry property of a data set. Furthermore, this framework is a general platform to develop new algorithm for dimensionality reduction. To this end, we propose a new supervised algorithm, Marginal Fisher Analysis (MFA), for dimensionality reduction by designing two graphs that characterize the intra-class compactness and inter-class separability, respectively. MFA measures the intra-class compactness with the distance between each data point and its neighboring points of the same class, and measures the inter-class separability with the class margins; thus it overcomes the limitations of traditional Linear Discriminant Analysis algorithm in terms of data distribution assumptions and available projection directions. The toy problem on artificial data and the real face recognition experiments both show the superiority of our proposed MFA in comparison to LDA.

关键词： Linear discriminant analysis Statistics Geometry Kernel Algorithm design and analysis Principal component analysis Laplace equations Asia Vectors Laboratories

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Concurrent subspaces analysis

Concurrent subspaces analysis

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Conference on Computer Vision and Pattern Recognition (CVPR)

作者： Dong Xu Shuicheng Yan Lei Zhang Hong-Jiang Zhang Zhengkai Liu Heung-Yeung Shum MOE-Microsoft Key Laboratory of Multimedia Computing and Communication & Department of EEIS University of Science and Technology Hefei Anhui China Department of Information Engineering Chinese University of Hong Kong Sha Tin Hong Kong China Microsoft Research Asia Beijing China

ISBN: (纸本)0769523722

A representative subspace is significant for image analysis, while the corresponding techniques often suffer from the curse of dimensionality dilemma. In this paper, we propose a new algorithm, called concurrent subspaces analysis (CSA), to derive representative subspaces by encoding image objects as 2/sup nd/ or even higher order tensors. In CSA, an original higher dimensional tensor is transformed into a lower dimensional one using multiple concurrent subspaces that characterize the most representative information of different dimensions, respectively. Moreover, an efficient procedure is provided to learn these subspaces in an iterative manner. As analyzed in this paper, each sub-step of CSA takes the column vectors of the matrices, which are acquired from the k-mode unfolding of the tensors, as the new objects to be analyzed, thus the curse of dimensionality dilemma can be effectively avoided. The extensive experiments on the 3/sup rd/ order tensor data, simulated video sequences and Gabor filtered digital number image database show that CSA outperforms principal component analysis in terms of both reconstruction and classification capability.

关键词： Tensile stress Image sequence analysis Image analysis Algorithm design and analysis Image coding Analytical models Video sequences Digital filters Gabor filters Image databases

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