The Modified Quasi-geostrophic Barotropic Models Based on Unsteady Topography

New models using scale analysis and perturbation methods were derivated starting from the shallow water equations based on barotropic fluids. In the paper, to discuss the irregular topography with different magnitudes, especially considering the condition of the vast terrain, some modified quasi-geostrophic barotropic models were obtained. The unsteady terrain is more suitable to describe the motion of the fluid state of the earth because of the change of global climate and environment, so the modified models are more rational potential vorticity equations. If we do not consider the influence of topography and other factors, the models degenerate to the general quasi-geostrophic barotropic equations in the previous studies

Multigrid Nonlocal Gaussian Mixture Model for Segmentation of Brain Tissues in Magnetic Resonance Images

We propose a novel segmentation method based on regional and nonlocal information to overcome the impact of image intensity inhomogeneities and noise in human brain magnetic resonance images. With the consideration of the spatial distribution of different tissues in brain images, our method does not need preestimation or precorrection procedures for intensity inhomogeneities and noise. A nonlocal information based Gaussian mixture model (NGMM) is proposed to reduce the effect of noise. To reduce the effect of intensity inhomogeneity, the multigrid nonlocal Gaussian mixture model (MNGMM) is proposed to segment brain MR images in each nonoverlapping multigrid generated by using a new multigrid generation method. Therefore the proposed model can simultaneously overcome the impact of noise and intensity inhomogeneity and automatically classify 2D and 3D MR data into tissues of white matter, gray matter, and cerebral spinal fluid. To maintain the statistical reliability and spatial continuity of the segmentation, a fusion strategy is adopted to integrate the clustering results from different grid. The experiments on synthetic and clinical brain MR images demonstrate the superior performance of the proposed model comparing with several state-of-the-art algorithms

A Novel 3D Anisotropic Total Variation Regularized Low Rank Method for Hyperspectral Image Mixed Denoising

Known to be structured in several patterns at the same time, the prior image of interest is always modeled with the idea of enforcing multiple constraints on unknown signals. For instance, when dealing with a hyperspectral restoration problem, the combination of constraints with piece-wise smoothness and low rank has yielded promising reconstruction results. In this paper, we propose a novel mixed-noise removal method by employing 3D anisotropic total variation and low rank constraints simultaneously for the problem of hyperspectral image (HSI) restoration. The main idea of the proposed method is based on the assumption that the spectra in an HSI lies in the same low rank subspace and both spatial and spectral domains exhibit the property of piecewise smoothness. The low rankness of an HSI is approximately exploited by the nuclear norm, while the spectral-spatial smoothness is explored using 3D anisotropic total variation (3DATV), which is defined as a combination of 2D spatial TV and 1D spectral TV of the HSI cube. Finally, the proposed restoration model is effectively solved by the alternating direction method of multipliers (ADMM). Experimental results of both simulated and real HSI datasets validate the superior performance of the proposed method in terms of quantitative assessment and visual quality

Hyperspectral Mixed Denoising via Spectral Difference-Induced Total Variation and Low-Rank Approximation

Exploration of multiple priors on observed signals has been demonstrated to be one of the effective ways for recovering underlying signals. In this paper, a new spectral difference-induced total variation and low-rank approximation (termed SDTVLA) method is proposed for hyperspectral mixed denoising. Spectral difference transform, which projects data into spectral difference space (SDS), has been proven to be powerful at changing the structures of noises (especially for sparse noise with a specific pattern, e.g., stripes or dead lines present at the same position in a series of bands) in an original hyperspectral image (HSI), thus allowing low-rank techniques to get rid of mixed noises more efficiently without treating them as low-rank features. In addition, because the neighboring pixels are highly correlated and the spectra of homogeneous objects in a hyperspectral scene are always in the same low-dimensional manifold, we are inspired to combine total variation and the nuclear norm to simultaneously exploit the local piecewise smoothness and global low rankness in SDS for mixed noise reduction of HSI. Finally, the alternating direction methods of multipliers (ADMM) is employed to effectively solve the SDTVLA model. Extensive experiments on three simulated and two real HSI datasets demonstrate that, in terms of quantitative metrics (i.e., the mean peak signal-to-noise ratio (MPSNR), the mean structural similarity index (MSSIM) and the mean spectral angle (MSA)), the proposed SDTVLA method is, on average, 1.5 dB higher MPSNR values than the competitive methods as well as performing better in terms of visual effect

Hyperspectral Classification via Superpixel Kernel Learning-Based Low Rank Representation

High dimensional image classification is a fundamental technique for information retrieval from hyperspectral remote sensing data. However, data quality is readily affected by the atmosphere and noise in the imaging process, which makes it difficult to achieve good classification performance. In this paper, multiple kernel learning-based low rank representation at superpixel level (Sp_MKL_LRR) is proposed to improve the classification accuracy for hyperspectral images. Superpixels are generated first from the hyperspectral image to reduce noise effect and form homogeneous regions. An optimal superpixel kernel parameter is then selected by the kernel matrix using a multiple kernel learning framework. Finally, a kernel low rank representation is applied to classify the hyperspectral image. The proposed method offers two advantages. (1) The global correlation constraint is exploited by the low rank representation, while the local neighborhood information is extracted as the superpixel kernel adaptively learns the high-dimensional manifold features of the samples in each class; (2) It can meet the challenges of multiscale feature learning and adaptive parameter determination in the conventional kernel methods. Experimental results on several hyperspectral image datasets demonstrate that the proposed method outperforms several state-of-the-art classifiers tested in terms of overall accuracy, average accuracy, and kappa statistic

Sparse Graph Embedding Based on the Fuzzy Set for Image Classification

In recent years, many face image feature extraction and dimensional reduction algorithms have been proposed for linear and nonlinear data, such as local-based graph embedding algorithms or fuzzy set algorithms. However, the aforementioned algorithms are not very effective for face images because they are always affected by overlaps (outliers) and sparsity points in the database. To solve the problems, a new and effective dimensional reduction method for face recognition is proposed—sparse graph embedding with the fuzzy set for image classification. The aim of this algorithm is to construct two new fuzzy Laplacian scattering matrices by using the local graph embedding and fuzzy k-nearest neighbor. Finally, the optimal discriminative sparse projection matrix is obtained by adding elastic network regression. Experimental results and analysis indicate that the proposed algorithm is more effective than other algorithms in the UCI wine dataset and ORL, Yale, and AR standard face databases

SSCNN-S: A Spectral-Spatial Convolution Neural Network with Siamese Architecture for Change Detection

In this paper, a spectral-spatial convolution neural network with Siamese architecture (SSCNN-S) for hyperspectral image (HSI) change detection (CD) is proposed. First, tensors are extracted in two HSIs recorded at different time points separately and tensor pairs are constructed. The tensor pairs are then incorporated into the spectral-spatial network to obtain two spectral-spatial vectors. Thereafter, the Euclidean distances of the two spectral-spatial vectors are calculated to represent the similarity of the tensor pairs. We use a Siamese network based on contrastive loss to train and optimize the network so that the Euclidean distance output by the network describes the similarity of tensor pairs as accurately as possible. Finally, the values obtained by inputting all tensor pairs into the trained model are used to judge whether a pixel belongs to the change area. SSCNN-S aims to transform the problem of HSI CD into a problem of similarity measurement for tensor pairs by introducing the Siamese network. The network used to extract tensor features in SSCNN-S combines spectral and spatial information to reduce the impact of noise on CD. Additionally, a useful four-test scoring method is proposed to improve the experimental efficiency instead of taking the mean value from multiple measurements. Experiments on real data sets have demonstrated the validity of the SSCNN-S method