A two-level Bregmanized method with graph regularized sparse coding (TBGSC) is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inne...A two-level Bregmanized method with graph regularized sparse coding (TBGSC) is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
In this paper, we designed a color visualization model for sparse representation of the whole hyperspectral image, in which, not only the spectral information in the sparse representation but also the spatial informat...In this paper, we designed a color visualization model for sparse representation of the whole hyperspectral image, in which, not only the spectral information in the sparse representation but also the spatial information of the whole image is retained. After the sparse representation, the color labels of the effective elements of the sparse coding dictionary are selected according to the sparse coefficient and then the mixed images are displayed. The generated images maintain spectral distance preservation and have good separability. For local ground objects, the proposed single-pixel mixed array and improved oriented sliver textures methods are integrated to display the specific composition of each pixel. This avoids the confusion of the color presentation in the mixed-pixel color display and can also be used to reconstruct the original hyperspectral data. Finally, the model effectiveness was proved using real data. This method is promising and can find use in many fields, such as energy exploration, environmental monitoring, disaster warning, and so on.展开更多
The K-COD (K-Complete Orthogonal Decomposition) algorithm for generating adaptive dictionary for signals sparse representation in the framework of K-means clustering is proposed in this paper,in which rank one approxi...The K-COD (K-Complete Orthogonal Decomposition) algorithm for generating adaptive dictionary for signals sparse representation in the framework of K-means clustering is proposed in this paper,in which rank one approximation for components assembling signals based on COD and K-means clustering based on chaotic random search are well utilized. The results of synthetic test and empirical experiment for the real data show that the proposed algorithm outperforms recently reported alternatives: K-Singular Value Decomposition (K-SVD) algorithm and Method of Optimal Directions (MOD) algorithm.展开更多
Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications. In this paper, we review two data-driven time-frequency analysis m...Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications. In this paper, we review two data-driven time-frequency analysis methods that we introduced recently to study trend and instantaneous frequency of nonlinear and nonstationary data. These methods are inspired by the empirical mode decomposition method (EMD) and the recently developed compressed (compressive) sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a(t) cos(0(t))}, where a is assumed to be less oscillatory than cos(θ(t)) and θ '≥ 0. This problem can be formulated as a nonlinear ι0 optimization problem. We have proposed two methods to solve this nonlinear optimization problem. The first one is based on nonlinear basis pursuit and the second one is based on nonlinear matching pursuit. Convergence analysis has been carried out for the nonlinear matching pursuit method. Some numerical experiments are given to demonstrate the effectiveness of the proposed methods.展开更多
基金The National Natural Science Foundation of China (No.61362001,61102043,61262084,20132BAB211030,20122BAB211015)the Basic Research Program of Shenzhen(No.JC201104220219A)
文摘A two-level Bregmanized method with graph regularized sparse coding (TBGSC) is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
基金supported by the National Natural Science Foundation of China (Grant No.61275010,61077079)the State Key Program of National Natural Science Foundation of Heilongjiang Province of China (No.ZD201216)the Fundamental Research Funds for the Central Universities (No.HEUCF130820)
文摘In this paper, we designed a color visualization model for sparse representation of the whole hyperspectral image, in which, not only the spectral information in the sparse representation but also the spatial information of the whole image is retained. After the sparse representation, the color labels of the effective elements of the sparse coding dictionary are selected according to the sparse coefficient and then the mixed images are displayed. The generated images maintain spectral distance preservation and have good separability. For local ground objects, the proposed single-pixel mixed array and improved oriented sliver textures methods are integrated to display the specific composition of each pixel. This avoids the confusion of the color presentation in the mixed-pixel color display and can also be used to reconstruct the original hyperspectral data. Finally, the model effectiveness was proved using real data. This method is promising and can find use in many fields, such as energy exploration, environmental monitoring, disaster warning, and so on.
基金Supported by the National Natural Science Foundation of China under Grants (No. 60872123 & U0835001)by Natural Science Foundation of Guangdong Province, China (No. 07006496)
文摘The K-COD (K-Complete Orthogonal Decomposition) algorithm for generating adaptive dictionary for signals sparse representation in the framework of K-means clustering is proposed in this paper,in which rank one approximation for components assembling signals based on COD and K-means clustering based on chaotic random search are well utilized. The results of synthetic test and empirical experiment for the real data show that the proposed algorithm outperforms recently reported alternatives: K-Singular Value Decomposition (K-SVD) algorithm and Method of Optimal Directions (MOD) algorithm.
基金supported by Air Force Ofce of Scientifc ResearchMultidisciplinary University Research Initiative+3 种基金USA(Grant No.FA9550-09-1-0613)Department of Energy of USA(Grant No.DE-FG02-06ER25727)Natural Science Foundation of USA(Grant No.DMS-0908546)National Natural Science Foundation of China(Grant No.11201257)
文摘Adaptive data analysis provides an important tool in extracting hidden physical information from multiscale data that arise from various applications. In this paper, we review two data-driven time-frequency analysis methods that we introduced recently to study trend and instantaneous frequency of nonlinear and nonstationary data. These methods are inspired by the empirical mode decomposition method (EMD) and the recently developed compressed (compressive) sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions of the form {a(t) cos(0(t))}, where a is assumed to be less oscillatory than cos(θ(t)) and θ '≥ 0. This problem can be formulated as a nonlinear ι0 optimization problem. We have proposed two methods to solve this nonlinear optimization problem. The first one is based on nonlinear basis pursuit and the second one is based on nonlinear matching pursuit. Convergence analysis has been carried out for the nonlinear matching pursuit method. Some numerical experiments are given to demonstrate the effectiveness of the proposed methods.