Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory

Zhu, Dan; Renaut, Rosemary A.; Li, Hongwei; Liu, Tianyou

doi:10.3934/ipi.2020076

Cited by 4 publications

(2 citation statements)

References 26 publications

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“…Within the separation of potential field data, low‐rank matrix decomposition methods based on the respective low‐rank and sparse trajectory matrices of magnetic anomalies generated by deep and shallow sources have been proposed (Zhu et al., 2020). High‐accuracy separation with strong robustness can be achieved by simultaneously minimizing the rank and ℓ 0 ‐norm of the regional and residual anomalies (Zhu et al., 2021). However, as in other separation methods, these low‐rank methods were designed to separate magnetic anomalies caused by sources at different depths; therefore, they cannot be applied to extract magnetic anomalies caused by sources that occur at similar depths.…”

Section: Introductionmentioning

confidence: 99%

Can Targeted Source Information Be Extracted From Superimposed Magnetic Anomalies?

Zhu

2022

JGR Solid Earth

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Magnetic anomalies commonly contain anomalies generated by crustal rocks that have variable mineral compositions and natural remanent magnetizations. Recovery of magnetic parameters from superimposed magnetic anomaly sources is therefore important for mineral exploration and geological studies. Superposition of magnetic anomalies leads to nonnegligible errors of inversion and interpretation. Therefore, extraction of magnetic anomalies is essential for magnetic data processing; however, existing methods cannot extract magnetic anomalies caused by sources without substantial depth differences. A novel low‐rank method is proposed for extracting a target magnetic anomaly from a superimposed anomaly. The low‐rank feature of the magnetic anomaly is used to obtain the target anomaly by reducing the Schatten‐p norm of the superimposed anomaly according to the possible target source distribution. The target magnetic anomaly can then be extracted from the data generated by the source interference at the same or different depths. The accuracy of the proposed method was verified using synthetic modeling. Magnetization vector information for individual igneous rocks was recovered from extracted magnetic anomalies via 3‐D inversion of field data from Yeshan (eastern China) that contain complex magnetic anomaly superpositions. The distributions and lithologies of five buried igneous rocks, including basalt, diabase, and granodiorite, were then identified. The proposed method expands the problem of separating magnetic information from rocks in different layers with large depth differences to rocks within the same or other layers and recovers geometric and physical information for each targeted magnetic source from the superimposed anomaly.

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Section: Introductionmentioning

confidence: 99%

Can Targeted Source Information Be Extracted From Superimposed Magnetic Anomalies?

Zhu

2022

JGR Solid Earth

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“…By combining CNN with MF, the ConvMF algorithm is obtained, which obtains predictive scores by inner product of the implicit factors of users' objects. In the ConvMF algorithm, CNN first converts the original information into a digital matrix, extracts its features, and finally obtains the final hidden factor representation through the fully connected layer [15,21,25]. The calculation formula for the final output vector is Equation (2).…”

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confidence: 99%

Design and Implementation of an English Learning System Based on Intelligent Recommendation

Yuan

2024

ITC

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The Internet has led to the rapid development of online education, but it has also caused redundancy in educational information. How to choose appropriate courses from a large number of online education resources has become a major problem for current learners. Therefore, the study proposes an English learning system based on efficient and deep Matrix decomposition. The results of the experiments showed that, in practical teaching applications, about 57.5% of students with good grades have improved their grades due to the use of the English learning system proposed by the research institute, with only about 17.5% of their grades decreasing. 67.5% of students with average grades have improved their grades after using the system, with only 10% decreasing. Among the students with poor grades, about 50% of them improved their academic performance through the system, while about 27.5% of them experienced a decrease. Meanwhile, the experiment also tested the efficient deep Matrix decomposition model in the learning system: the minimum absolute average errors of the model on different data sets are about 0.61, 0.69, 0.77 and 0.82, respectively. The minimum Root-mean-square deviation is about 0.91, 0.98, 1.06 and 1.1, which is far lower than other recommended models. The above results show that the system constructed in this paper can recommend courses accordingto students ‘actual learning level, and can effectively improve students’ academic performance in the actual teaching process.

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Gravity inversion usingL0 norm for sparse constraints

Zhu,

Hu,

Liu

et al. 2023

Geophysical Journal International

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SUMMARY Gravity surveys constitute an important method for investigating the Earth's interior based on density contrasts related to Earth material differentials. Because lithology depends on the environment and the period of formation, there are generally clear boundaries between rocks with different lithologies. Inversions with convex functions for approximating the L0 norm are used to detect boundaries in reconstructed models. Optimizations can easily be found because of the convex transformations; however, the volume of the reconstructed model depends on the weighting parameter and the density constraint rather than the model sparsity. To determine and adapt the modelling size, a novel non-convex framework for gravity inversion is proposed. The proposed optimization aims to directly reduce the L0 norm of the density matrix. An improved iterative hard thresholding algorithm is developed to linearly reduce the L0 penalty during the inner iteration. Accordingly, it is possible to determine the modelling scale during the iteration and achieve an expected scale for the reconstructed model. Both simple and complex model experiments demonstrate that the proposed method efficiently reconstructs models. In addition, granites formed during the Yanshanian and Indosinian periods in the Nanling region, China, are reconstructed according to the modelling size evaluated in agreement with the magnetotelluric profile and density statistics of rock samples. The known ores occur at the contact zones between the sedimentary rocks and the reconstructed Yanshanian granites. The ore-forming bodies, periods, and processes are identified, providing guidance for further deep resource exploration in the study area.

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Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory

Cited by 4 publications

References 26 publications

Can Targeted Source Information Be Extracted From Superimposed Magnetic Anomalies?

Can Targeted Source Information Be Extracted From Superimposed Magnetic Anomalies?

Design and Implementation of an English Learning System Based on Intelligent Recommendation

Gravity inversion usingL0 norm for sparse constraints

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