Spatial Distribution of Lead (Pb) in Soil: A Case Study in a Contaminated Area of the Czech Republic

For decades, the Příbram district in the Czech Republic has been affected by industrial and mining activities. These activities are important sources of heavy metal pollutants that are detrimental to soil quality. A recent study examined visible–near-infrared (VNIR), shortwave-infrared (SWIR) and X-ray fluorescence (XRF) spectroscopy to model soil lead (Pb) content in a selected area located in the Příbram district. Following that study, and using the same chemical and geographical data, we examined the spatial distribution of Pb content in the soil, with a combination of different traditional spatial analyses (Moran’s I, hotspot analysis, and Kriging) that were significantly validated. One of the novel points of this work is the use of the Getis–Ord hotspot analysis before the execution of a Kriging interpolation model to better emphasize clustering patterns. The results indicated that Pb was a spatially dependent soil property and through extensive in situ sampling, it was possible to generate a very accurate Kriging interpolation model. The high-Pb hotspots coincided with topographic obstacles that were modeled using topographic profiles extracted from the open-source Google Earth platform, indicating that Pb content does not always exhibit a direct relationship with topographic height as a result of runoff, due to the contribution of topographic steps. This observation provides a new perspective on the relationship between Pb content and topographic patterns.

Comparing different metrics on an anisotropic depth completion model

This paper discussed an anisotropic interpolation model that filling in-depth data in a largely empty region of a depth map. We consider an image with an anisotropic metric gi⁢j that incorporates spatial and photometric data. We propose a numerical implementation of our model based on the “eikonal” operator, which compute the solution of a degenerated partial differential equation (the biased Infinity Laplacian or biased Absolutely Minimizing Lipschitz Extension). This equation’s solution creates exponential cones based on the available data, extending the available depth data and completing the depth map image. Because of this, this operator is better suited to interpolating smooth surfaces. To perform this task, we assume we have at our disposal a reference color image and a depth map. We carried out an experimental comparison of the AMLE and bAMLE using various metrics with square root, absolute value, and quadratic terms. In these experiments, considered color spaces were sRGB, XYZ, CIE-L*⁢a*⁢b*, and CMY. In this document, we also presented a proposal to extend the AMLE and bAMLE to the time domain. Finally, in the parameter estimation of the model, we compared EHO and PSO. The combination of sRGB and square root metric produces the best results, demonstrating that our bAMLE model outperforms the AMLE model and other contemporary models in the KITTI depth completion suite dataset. This type of model, such as AMLE and bAMLE, is simple to implement and represents a low-cost implementation option for similar applications.

Robust high-dimensional seismic data interpolation based on elastic half norm regularization and tensor dictionary learning

Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image under-ground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or under-sampled data. Under the framework of compressed sensing, we propose a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the Elastic-Net, we first develop the elastic half norm regularization as a sparsity constraint, and establish a robust high-dimensional interpolation model with this technique. Then, considering the multi-dimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that, this method has superior performance and higher computational efficiency in both noise-free and noisy seismic data interpolation, compared to extensively utilized dictionary learning-based interpolation methods.