Difference Curvature Multidimensional Network for Hyperspectral Image Super-Resolution

In recent years, convolutional-neural-network-based methods have been introduced to the field of hyperspectral image super-resolution following their great success in the field of RGB image super-resolution. However, hyperspectral images appear different from RGB images in that they have high dimensionality, implying a redundancy in the high-dimensional space. Existing approaches struggle in learning the spectral correlation and spatial priors, leading to inferior performance. In this paper, we present a difference curvature multidimensional network for hyperspectral image super-resolution that exploits the spectral correlation to help improve the spatial resolution. Specifically, we introduce a multidimensional enhanced convolution (MEC) unit into the network to learn the spectral correlation through a self-attention mechanism. Meanwhile, it reduces the redundancy in the spectral dimension via a bottleneck projection to condense useful spectral features and reduce computations. To remove the unrelated information in high-dimensional space and extract the delicate texture features of a hyperspectral image, we design an additional difference curvature branch (DCB), which works as an edge indicator to fully preserve the texture information and eliminate the unwanted noise. Experiments on three publicly available datasets demonstrate that the proposed method can recover sharper images with minimal spectral distortion compared to state-of-the-art methods. PSNR/SAM is 0.3–0.5 dB/0.2–0.4 better than the second best methods.

Fractional-order difference curvature-driven fractional anisotropic diffusion equation for image super-resolution

Image super-resolution methods-based existing edge indicating operators — namely Gauss curvature, mean curvature and gradient — cannot effectively identify the edges, ramps and flat regions and suffer from the loss of fine textures. To address these issues, this paper presents a fractional anisotropic diffusion equation based on a new edge indicator, named fractional-order difference curvature, which can characterize the intensity variations in images. We introduce the frequency-domain definition for fractional-order derivative by the Fourier transform, which is easy to implement numerically. The new edge indicator is better than the existing edge indicating operators in distinguishing between ramps and edges and can better handle the fine textures. Comparative results for natural images validate that the proposed method can yield a visually pleasing result and better values of MSSIM and PSNR.

Tank Car Sloshing on Rail Transportation Safety Under Various Loading, Track and In-Train Force Conditions

Analytical work was conducted to study if movement of liquid in a tank car (or sloshing) could contribute in any way to derailments of trains carrying dangerous goods liquids. A liquid sloshing model was developed for railway tank car with formulas generated based on available finite element analysis data. An empty tank car dynamics simulation model validated with measured data was used as the base model to implement the liquid sloshing model. Hundreds of thousands of dynamics simulations were conducted for the tank car with liquid cargo at various fill ratios and with equivalent solid (i.e., rigid) cargo on more than 1000 measured curves. The results show that under some conditions tank car sloshing could increase the risk of derailment. The detrimental effect of tank car sloshing on rail safety increases with the increase of outage, trailing tonnage, grade, car length difference, curvature, train speed and track geometry irregularities. Quantitative risk analysis could be improved by considering the effects of tank car sloshing on derailment risk. The findings can be used by regulators and the railroads to improve train marshalling practice and risk mapping of railway networks.

Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising

The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.

Image Structure-Preserving Denoising Based on Difference Curvature Driven Fractional Nonlinear Diffusion

The traditional integer-order partial differential equations and gradient regularization based image denoising techniques often suffer from staircase effect, speckle artifacts, and the loss of image contrast and texture details. To address these issues, in this paper, a difference curvature driven fractional anisotropic diffusion for image noise removal is presented, which uses two new techniques, fractional calculus and difference curvature, to describe the intensity variations in images. The fractional-order derivatives information of an image can deal well with the textures of the image and achieve a good tradeoff between eliminating speckle artifacts and restraining staircase effect. The difference curvature constructed by the second order derivatives along the direction of gradient of an image and perpendicular to the gradient can effectively distinguish between ramps and edges. Fourier transform technique is also proposed to compute the fractional-order derivative. Experimental results demonstrate that the proposed denoising model can avoid speckle artifacts and staircase effect and preserve important features such as curvy edges, straight edges, ramps, corners, and textures. They are obviously superior to those of traditional integral based methods. The experimental results also reveal that our proposed model yields a good visual effect and better values of MSSIM and PSNR.