sampling pattern
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Minerals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1431
Author(s):  
Justyna Auguścik-Górajek ◽  
Jacek Mucha ◽  
Monika Wasilewska-Błaszczyk ◽  
Wojciech Kaczmarek

As a result of the exploitation of ore deposits, in addition to the main elements, the accompanying elements are also partially recovered. Some of them increase the profitability of exploitation, while others reduce it because they hinder the recovery of the main elements and thus increase the costs of the recovery process. A comprehensive economic calculation to assess the profitability of ore mining depends on an appropriately accurate estimation of the resources of both the main and associated elements. This issue was analyzed with the example of the Cu-Ag Rudna ore deposit (LGCD, Poland). The subject of the assessment was the resources prediction accuracy of the main element (Cu) and four (4) accompanying elements (Co, Ni, Pb, and V) using geostatistical estimation method, in particular the ordinary kriging after the estimation of the relative variograms for describing the spatial variability structures of elements abundance. It was found that the standard kriging errors (deviations) in accompanying elements resources that are scheduled for exploitation within a one-year period in some parts of deposits are drastically greater (2 to 5 times) than the estimation errors of the main element resources. This is due to the sparse sampling pattern for their determinations and/or the high variability (among others nugget effect) of their abundance. In this situation, without additional sampling and a denser sampling pattern, the possibilities of a reliable assessment of the influence of accompanying elements on the economic consequences of exploitation are very limited.


Author(s):  
D. Orynbassar ◽  
N. Madani

This work addresses the problem of geostatistical simulation of cross-correlated variables by factorization approaches in the case when the sampling pattern is unequal. A solution is presented, based on a Co-Gibbs sampler algorithm, by which the missing values can be imputed. In this algorithm, a heterotopic simple cokriging approach is introduced to take into account the cross-dependency of the undersampled variable with the secondary variable that is more available over the entire region. A real gold deposit is employed to test the algorithm. The imputation results are compared with other Gibbs sampler techniques for which simple cokriging and simple kriging are used. The results show that heterotopic simple cokriging outperforms the other two techniques. The imputed values are then employed for the purpose of resource estimation by using principal component analysis (PCA) as a factorization technique, and the output compared with traditional factorization approaches where the heterotopic part of the data is removed. Comparison of the results of these two techniques shows that the latter leads to substantial losses of important information in the case of an unequal sampling pattern, while the former is capable of reproducing better recovery functions.


Author(s):  
Maximilian Gram ◽  
Daniel Gensler ◽  
Patrick Winter ◽  
Michael Seethaler ◽  
Paula Anahi Arias-Loza ◽  
...  

Abstract Purpose T1ρ dispersion quantification can potentially be used as a cardiac magnetic resonance index for sensitive detection of myocardial fibrosis without the need of contrast agents. However, dispersion quantification is still a major challenge, because T1ρ mapping for different spin lock amplitudes is a very time consuming process. This study aims to develop a fast and accurate T1ρ mapping sequence, which paves the way to cardiac T1ρ dispersion quantification within the limited measurement time of an in vivo study in small animals. Methods A radial spin lock sequence was developed using a Bloch simulation-optimized sampling pattern and a view-sharing method for image reconstruction. For validation, phantom measurements with a conventional sampling pattern and a gold standard sequence were compared to examine T1ρ quantification accuracy. The in vivo validation of T1ρ mapping was performed in N = 10 mice and in a reproduction study in a single animal, in which ten maps were acquired in direct succession. Finally, the feasibility of myocardial dispersion quantification was tested in one animal. Results The Bloch simulation-based sampling shows considerably higher image quality as well as improved T1ρ quantification accuracy (+ 56%) and precision (+ 49%) compared to conventional sampling. Compared to the gold standard sequence, a mean deviation of − 0.46 ± 1.84% was observed. The in vivo measurements proved high reproducibility of myocardial T1ρ mapping. The mean T1ρ in the left ventricle was 39.5 ± 1.2 ms for different animals and the maximum deviation was 2.1% in the successive measurements. The myocardial T1ρ dispersion slope, which was measured for the first time in one animal, could be determined to be 4.76 ± 0.23 ms/kHz. Conclusion This new and fast T1ρ quantification technique enables high-resolution myocardial T1ρ mapping and even dispersion quantification within the limited time of an in vivo study and could, therefore, be a reliable tool for improved tissue characterization.


2021 ◽  
Vol 7 (7) ◽  
pp. 110
Author(s):  
Zehan Chao ◽  
Longxiu Huang ◽  
Deanna Needell

Matrix completion, the problem of completing missing entries in a data matrix with low-dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog that attempts to impute missing tensor entries from similar low-rank type assumptions. In this paper, we study the tensor completion problem when the sampling pattern is deterministic and possibly non-uniform. We first propose an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm for the recovery of the underlying low-rank tensor from noisy observations and then derive the error bounds under a properly weighted metric. Additionally, the efficiency and accuracy of our algorithm are both tested using synthetic and real datasets in numerical simulations.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jinhua Sheng ◽  
Yuchen Shi ◽  
Qiao Zhang

AbstractGeneralized auto-calibrating partially parallel acquisitions (GRAPPA) and other parallel Magnetic Resonance Imaging (pMRI) methods restore the unacquired data in k-space by linearly calculating the undersampled data around the missing points. In order to obtain the weight of the linear calculation, a small number of auto-calibration signal (ACS) lines need to be sampled at the center of the k-space. Therefore, the sampling pattern used in this type of method is to full sample data in the middle area and undersample in the outer k-space with nominal reduction factors. In this paper, we propose a novel reconstruction method with a multiple variable density sampling (MVDS) that is different from traditional sampling patterns. Our method can significantly improve the image quality using multiple reduction factors with fewer ACS lines. Specifically, the traditional sampling pattern only uses a single reduction factor to uniformly undersample data in the region outside the ACS, but we use multiple reduction factors. When sampling the k-space data, we keep the ACS lines unchanged, use a smaller reduction factor for undersampling data near the ACS lines and a larger reduction factor for the outermost part of k-space. The error is lower after reconstruction of this region by undersampled data with a smaller reduction factor. The experimental results show that with the same amount of data sampled, using NL-GRAPPA to reconstruct the k-space data sampled by our method can result in lower noise and fewer artifacts than traditional methods. In particular, our method is extremely effective when the number of ACS lines is small.


2021 ◽  
pp. 232-242
Author(s):  
Jinwei Zhang ◽  
Hang Zhang ◽  
Chao Li ◽  
Pascal Spincemaille ◽  
Mert Sabuncu ◽  
...  

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