The Experts below are selected from a list of 83061 Experts worldwide ranked by ideXlab platform
Wei Zhu - One of the best experts on this subject based on the ideXlab platform.
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hyperspectral anomaly detection via global and local joint modeling of background
IEEE Transactions on Signal Processing, 2019Co-Authors: Wei Zhu, Jocelyn Chanussot, Stanley OsherAbstract:Anomaly detection is a hot topic in hyperspectral signal processing. The key point of hyperspectral anomaly detection is the modeling of the background. In this paper, we propose a novel anomaly detection method via global and local joint modeling of background. Based on the observation that the local three-Dimensional patch belonging to the background in hyperspectral image (HSI) usually lies in a low Dimensional Manifold, we propose to reconstruct the background part of a HSI from its subsample by scalable low Dimensional Manifold modeling (SLDMM). Thus, the background of HSI can be well characterized in both global and local aspects. Taking into consideration that the SLDMM reconstructs the background part at a low sampling ratio, we propose a multiple random sampling reconstruction strategy to further improve the detection accuracies and robustness. The final background is generated by the mean of backgrounds reconstructed from the multiple random sampling and the anomalies are contained in the residual between the observed HSI and the mean background. Experimental results on three real datasets demonstrate that the proposed anomaly detection method outperforms other state-of-the-art hyperspectral anomaly detection methods.
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scalable low Dimensional Manifold model in the reconstruction of noisy and incomplete hyperspectral images
Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2018Co-Authors: Wei Zhu, Zuoqiang Shi, Stanley OsherAbstract:We present a scalable low Dimensional Manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to a collection of low Dimensional Manifolds. To emphasize this, the dimension of the Manifold is directly used as a regularizer in a variational functional, which is solved efficiently by alternating direction of minimization and weighted nonlocal Laplacian. Unlike general 3D images, the same similarity matrix can be shared across all spectral bands for a hyperspectral image, therefore the resulting algorithm is much more scalable than that for general 3D data [1]. Numerical experiments on the reconstruction of hyperspectral images from sparse and noisy sampling demonstrate the superiority of our proposed algorithm in terms of both speed and accuracy.
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ldmnet low Dimensional Manifold regularized neural networks
Computer Vision and Pattern Recognition, 2018Co-Authors: Wei Zhu, Qiang Qiu, Jiaji Huang, Robert Calderbank, Guillermo Sapiro, Ingrid DaubechiesAbstract:Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing overfitting are data-independent. Data-dependent regularizations are mostly motivated by the observation that data of interest lie close to a Manifold, which is typically hard to parametrize explicitly. These methods usually only focus on the geometry of the input data, and do not necessarily encourage the networks to produce geometrically meaningful features. To resolve this, we propose the Low-Dimensional-Manifold-regularized neural Network (LDMNet), which incorporates a feature regularization method that focuses on the geometry of both the input data and the output features. In LDMNet, we regularize the network by encouraging the combination of the input data and the output features to sample a collection of low Dimensional Manifolds, which are searched efficiently without explicit parametrization. To achieve this, we directly use the Manifold dimension as a regularization term in a variational functional. The resulting Euler-Lagrange equation is a Laplace-Beltrami equation over a point cloud, which is solved by the point integral method without increasing the computational complexity. In the experiments, we show that LDMNet significantly outperforms widely-used regularizers. Moreover, LDMNet can extract common features of an object imaged via different modalities, which is very useful in real-world applications such as cross-spectral face recognition.
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generalization of the weighted nonlocal laplacian in low Dimensional Manifold model
Journal of Scientific Computing, 2018Co-Authors: Zuoqiang Shi, Stanley Osher, Wei ZhuAbstract:In this paper we use the idea of the weighted nonlocal Laplacian (Shi et al. in J Sci Comput, 2017) to deal with the constraints in the low Dimensional Manifold model (Osher et al. in SIAM J Imaging Sci, 2017). In the original LDMM, the constraints are enforced by the point integral method. The point integral method provides a correct way to deal with the constraints, however it is not very efficient due to the fact that the symmetry of the original Laplace–Beltrami operator is destroyed. WNLL provides another way to enforce the constraints in LDMM. In WNLL, the discretized system is symmetric and sparse and hence it can be solved very fast. Our experimental results show that the computational cost is reduced significantly with the help of WNLL. Moreover, the results in image inpainting and denoising are also better than the original LDMM and competitive with state-of-the-art methods.
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scientific data interpolation with low Dimensional Manifold model
Journal of Computational Physics, 2018Co-Authors: Wei Zhu, Bao Wang, Richard C Barnard, Cory D Hauck, F Jenko, Stanley OsherAbstract:Abstract We propose to apply a low Dimensional Manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low Dimensionality of the patch Manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the Manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
Stanley Osher - One of the best experts on this subject based on the ideXlab platform.
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hyperspectral anomaly detection via global and local joint modeling of background
IEEE Transactions on Signal Processing, 2019Co-Authors: Wei Zhu, Jocelyn Chanussot, Stanley OsherAbstract:Anomaly detection is a hot topic in hyperspectral signal processing. The key point of hyperspectral anomaly detection is the modeling of the background. In this paper, we propose a novel anomaly detection method via global and local joint modeling of background. Based on the observation that the local three-Dimensional patch belonging to the background in hyperspectral image (HSI) usually lies in a low Dimensional Manifold, we propose to reconstruct the background part of a HSI from its subsample by scalable low Dimensional Manifold modeling (SLDMM). Thus, the background of HSI can be well characterized in both global and local aspects. Taking into consideration that the SLDMM reconstructs the background part at a low sampling ratio, we propose a multiple random sampling reconstruction strategy to further improve the detection accuracies and robustness. The final background is generated by the mean of backgrounds reconstructed from the multiple random sampling and the anomalies are contained in the residual between the observed HSI and the mean background. Experimental results on three real datasets demonstrate that the proposed anomaly detection method outperforms other state-of-the-art hyperspectral anomaly detection methods.
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scalable low Dimensional Manifold model in the reconstruction of noisy and incomplete hyperspectral images
Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing, 2018Co-Authors: Wei Zhu, Zuoqiang Shi, Stanley OsherAbstract:We present a scalable low Dimensional Manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to a collection of low Dimensional Manifolds. To emphasize this, the dimension of the Manifold is directly used as a regularizer in a variational functional, which is solved efficiently by alternating direction of minimization and weighted nonlocal Laplacian. Unlike general 3D images, the same similarity matrix can be shared across all spectral bands for a hyperspectral image, therefore the resulting algorithm is much more scalable than that for general 3D data [1]. Numerical experiments on the reconstruction of hyperspectral images from sparse and noisy sampling demonstrate the superiority of our proposed algorithm in terms of both speed and accuracy.
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generalization of the weighted nonlocal laplacian in low Dimensional Manifold model
Journal of Scientific Computing, 2018Co-Authors: Zuoqiang Shi, Stanley Osher, Wei ZhuAbstract:In this paper we use the idea of the weighted nonlocal Laplacian (Shi et al. in J Sci Comput, 2017) to deal with the constraints in the low Dimensional Manifold model (Osher et al. in SIAM J Imaging Sci, 2017). In the original LDMM, the constraints are enforced by the point integral method. The point integral method provides a correct way to deal with the constraints, however it is not very efficient due to the fact that the symmetry of the original Laplace–Beltrami operator is destroyed. WNLL provides another way to enforce the constraints in LDMM. In WNLL, the discretized system is symmetric and sparse and hence it can be solved very fast. Our experimental results show that the computational cost is reduced significantly with the help of WNLL. Moreover, the results in image inpainting and denoising are also better than the original LDMM and competitive with state-of-the-art methods.
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scientific data interpolation with low Dimensional Manifold model
Journal of Computational Physics, 2018Co-Authors: Wei Zhu, Bao Wang, Richard C Barnard, Cory D Hauck, F Jenko, Stanley OsherAbstract:Abstract We propose to apply a low Dimensional Manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low Dimensionality of the patch Manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the Manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
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low Dimensional Manifold model for image processing
Siam Journal on Imaging Sciences, 2017Co-Authors: Stanley Osher, Zuoqiang Shi, Wei ZhuAbstract:In this paper, we propose a novel low Dimensional Manifold model (LDMM) and apply it to some image processing problems. LDMM is based on the fact that the patch Manifolds of many natural images have low Dimensional structure. Based on this fact, the dimension of the patch Manifold is used as a regularization to recover the image. The key step in LDMM is to solve a Laplace--Beltrami equation over a point cloud which is solved by the point integral method. The point integral method enforces the sample point constraints correctly and gives better results than the standard graph Laplacian. Numerical simulations in image denoising, inpainting, and superresolution problems show that LDMM is a powerful method in image processing.
Cheng Yang - One of the best experts on this subject based on the ideXlab platform.
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3d point cloud denoising using graph laplacian regularization of a low Dimensional Manifold model
IEEE Transactions on Image Processing, 2020Co-Authors: Jin Zeng, Gene Cheung, Jiahao Pang, Cheng YangAbstract:3D point cloud—a new signal representation of volumetric objects—is a discrete collection of triples marking exterior object surface locations in 3D space. Conventional imperfect acquisition processes of 3D point cloud—e.g., stereo-matching from multiple viewpoint images or depth data acquired directly from active light sensors—imply non-negligible noise in the data. In this paper, we extend a previously proposed low-Dimensional Manifold model for the image patches to surface patches in the point cloud, and seek self-similar patches to denoise them simultaneously using the patch Manifold prior. Due to discrete observations of the patches on the Manifold, we approximate the Manifold dimension computation defined in the continuous domain with a patch-based graph Laplacian regularizer, and propose a new discrete patch distance measure to quantify the similarity between two same-sized surface patches for graph construction that is robust to noise. We show that our graph Laplacian regularizer leads to speedy implementation and has desirable numerical stability properties given its natural graph spectral interpretation. Extensive simulation results show that our proposed denoising scheme outperforms state-of-the-art methods in objective metrics and better preserves visually salient structural features like edges.
Jin Zeng - One of the best experts on this subject based on the ideXlab platform.
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3d point cloud denoising using graph laplacian regularization of a low Dimensional Manifold model
IEEE Transactions on Image Processing, 2020Co-Authors: Jin Zeng, Gene Cheung, Jiahao Pang, Cheng YangAbstract:3D point cloud—a new signal representation of volumetric objects—is a discrete collection of triples marking exterior object surface locations in 3D space. Conventional imperfect acquisition processes of 3D point cloud—e.g., stereo-matching from multiple viewpoint images or depth data acquired directly from active light sensors—imply non-negligible noise in the data. In this paper, we extend a previously proposed low-Dimensional Manifold model for the image patches to surface patches in the point cloud, and seek self-similar patches to denoise them simultaneously using the patch Manifold prior. Due to discrete observations of the patches on the Manifold, we approximate the Manifold dimension computation defined in the continuous domain with a patch-based graph Laplacian regularizer, and propose a new discrete patch distance measure to quantify the similarity between two same-sized surface patches for graph construction that is robust to noise. We show that our graph Laplacian regularizer leads to speedy implementation and has desirable numerical stability properties given its natural graph spectral interpretation. Extensive simulation results show that our proposed denoising scheme outperforms state-of-the-art methods in objective metrics and better preserves visually salient structural features like edges.
Barbara E Engelhardt - One of the best experts on this subject based on the ideXlab platform.
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a robust nonlinear low Dimensional Manifold for single cell rna seq data
BMC Bioinformatics, 2020Co-Authors: Archit Verma, Barbara E EngelhardtAbstract:Modern developments in single-cell sequencing technologies enable broad insights into cellular state. Single-cell RNA sequencing (scRNA-seq) can be used to explore cell types, states, and developmental trajectories to broaden our understanding of cellular heterogeneity in tissues and organs. Analysis of these sparse, high-Dimensional experimental results requires dimension reduction. Several methods have been developed to estimate low-Dimensional embeddings for filtered and normalized single-cell data. However, methods have yet to be developed for unfiltered and unnormalized count data that estimate uncertainty in the low-Dimensional space. We present a nonlinear latent variable model with robust, heavy-tailed error and adaptive kernel learning to estimate low-Dimensional nonlinear structure in scRNA-seq data. Gene expression in a single cell is modeled as a noisy draw from a Gaussian process in high dimensions from low-Dimensional latent positions. This model is called the Gaussian process latent variable model (GPLVM). We model residual errors with a heavy-tailed Student’s t-distribution to estimate a Manifold that is robust to technical and biological noise found in normalized scRNA-seq data. We compare our approach to common dimension reduction tools across a diverse set of scRNA-seq data sets to highlight our model’s ability to enable important downstream tasks such as clustering, inferring cell developmental trajectories, and visualizing high throughput experiments on available experimental data. We show that our adaptive robust statistical approach to estimate a nonlinear Manifold is well suited for raw, unfiltered gene counts from high-throughput sequencing technologies for visualization, exploration, and uncertainty estimation of cell states.
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a robust nonlinear low Dimensional Manifold for single cell rna seq data
bioRxiv, 2018Co-Authors: Archit Verma, Barbara E EngelhardtAbstract:Modern developments in single cell sequencing technologies enable broad insights into cellular state. Single cell RNA sequencing (scRNA-seq) can be used to explore cell types, states, and developmental trajectories to broaden understanding of cell heterogeneity in tissues and organs. Analysis of these sparse, high-Dimensional experimental results requires dimension reduction. Several methods have been developed to estimate low-Dimensional embeddings for filtered and normalized single cell data. However, methods have yet to be developed for unfiltered and unnormalized count data. We present a nonlinear latent variable model with robust, heavy-tailed error and adaptive kernel learning to estimate low-Dimensional nonlinear structure in scRNA-seq data. Gene expression in a single cell is modeled as a noisy draw from a Gaussian process in high dimensions from low-Dimensional latent positions. This model is called the Gaussian process latent variable model (GPLVM). We model residual errors with a heavy-tailed Student's t-distribution to estimate a Manifold that is robust to technical and biological noise. We compare our approach to common dimension reduction tools to highlight our model's ability to enable important downstream tasks, including clustering and inferring cell developmental trajectories, on available experimental data. We show that our robust nonlinear Manifold is well suited for raw, unfiltered gene counts from high throughput sequencing technologies for visualization and exploration of cell states.