Convergence of the Fourier-Galerkin spectral method for the Boltzmann equation with uncertainties

It is well-known that the Fourier-Galerkin spectral method has been a popular approach for the numerical approximation of the deterministic Boltzmann equation with spectral accuracy rigorously proved. In this paper, we will show that such a spectral convergence of the Fourier-Galerkin spectral method also holds for the Boltzmann equation with uncertainties arising from both collision kernel and initial condition. Our proof is based on newly-established spaces and norms that are carefully designed and take the velocity variable and random variables with their high regularities into account altogether. For future studies, this theoretical result will provide a solid foundation for further showing the convergence of the full-discretized system where both the velocity and random variables are discretized simultaneously

A Multiscale Deeply Described Correlatons-Based Model for Land-Use Scene Classification

Research efforts in land-use scene classification is growing alongside the popular use of High-Resolution Satellite (HRS) images. The complex background and multiple land-cover classes or objects, however, make the classification tasks difficult and challenging. This article presents a Multiscale Deeply Described Correlatons (MDDC)-based algorithm which incorporates appearance and spatial information jointly at multiple scales for land-use scene classification to tackle these problems. Specifically, we introduce a convolutional neural network to learn and characterize the dense convolutional descriptors at different scales. The resulting multiscale descriptors are used to generate visual words by a general mapping strategy and produce multiscale correlograms of visual words. Then, an adaptive vector quantization of multiscale correlograms, termed multiscale correlatons, are applied to encode the spatial arrangement of visual words at different scales. Experiments with two publicly available land-use scene datasets demonstrate that our MDDC model is discriminative for efficient representation of land-use scene images, and achieves competitive classification results with state-of-the-art methods

A Multiscale Deeply Described Correlatons-Based Model for Land-Use Scene Classification

Research efforts in land-use scene classification is growing alongside the popular use of High-Resolution Satellite (HRS) images. The complex background and multiple land-cover classes or objects, however, make the classification tasks difficult and challenging. This article presents a Multiscale Deeply Described Correlatons (MDDC)-based algorithm which incorporates appearance and spatial information jointly at multiple scales for land-use scene classification to tackle these problems. Specifically, we introduce a convolutional neural network to learn and characterize the dense convolutional descriptors at different scales. The resulting multiscale descriptors are used to generate visual words by a general mapping strategy and produce multiscale correlograms of visual words. Then, an adaptive vector quantization of multiscale correlograms, termed multiscale correlatons, are applied to encode the spatial arrangement of visual words at different scales. Experiments with two publicly available land-use scene datasets demonstrate that our MDDC model is discriminative for efficient representation of land-use scene images, and achieves competitive classification results with state-of-the-art methods

Multi-Task Joint Sparse and Low-Rank Representation for the Scene Classification of High-Resolution Remote Sensing Image

Scene classification plays an important role in the intelligent processing of High-Resolution Satellite (HRS) remotely sensed images. In HRS image classification, multiple features, e.g., shape, color, and texture features, are employed to represent scenes from different perspectives. Accordingly, effective integration of multiple features always results in better performance compared to methods based on a single feature in the interpretation of HRS images. In this paper, we introduce a multi-task joint sparse and low-rank representation model to combine the strength of multiple features for HRS image interpretation. Specifically, a multi-task learning formulation is applied to simultaneously consider sparse and low-rank structures across multiple tasks. The proposed model is optimized as a non-smooth convex optimization problem using an accelerated proximal gradient method. Experiments on two public scene classification datasets demonstrate that the proposed method achieves remarkable performance and improves upon the state-of-art methods in respective applications

A communication-efficient distributed deep learning remote sensing image change detection framework

With the introduction of deep learning methods, the computation required for remote sensing change detection has significantly increased, and distributed computing is applied to remote sensing change detection to improve computational efficiency. However, due to the large size of deep learning models, the time-consuming gradient transfer during distributed model training weakens the acceleration effectiveness in change detection. Data communication and updates can be the bottlenecks in distributed change detection systems with limited network resources. To address the interrelated problems, we propose a communication-efficient distributed deep learning remote sensing change detection framework (CEDD-CD) based on the synchronous update architecture. The CEDD-CD integrates change detection with communication-efficient distributed gradient compression approaches, which can efficiently reduce the data volume to be transferred. In addition, for the implicit effect caused by the delay of compressed gradient update, a momentum compensation mechanism under theoretical analysis was constructed to reduce the time consumption required for model convergence and strengthen the stability of distributed training. We also designed a unified distributed change detection system architecture to reduce the complexity of distributed modeling. Experiments were conducted on three datasets; the qualitative and quantitative results demonstrate that the CEDD-CD was effective for massive remote sensing image change detection