Articles published on Constrained Energy Minimization
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- Research Article
- 10.3390/min16020220
- Feb 22, 2026
- Minerals
- Khurram Riaz + 8 more
The McMurdo Dry Valleys (DVs) of South Victoria Land, Antarctica, constitute the largest ice-free region on the continent and one of Earth’s most Mars-analog environments. Their hyper-arid polar desert conditions offer a unique setting for investigating surface weathering and mineralogical processes under extreme climates. This study presents the first regional-scale mapping of alteration and crystalline weathering minerals across the McMurdo DVs. It uses Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) multispectral data; visible and near-infrared (VNIR) and shortwave infrared (SWIR) bands were analyzed through a Spectral Hourglass Workflow, endmember extraction, and spectral unmixing with Matched Filtering (MF) and Constrained Energy Minimization (CEM). Inter-algorithm consistency analysis between MF and CEM yielded 78.83% overall agreement with a Kappa coefficient of 0.75, indicating strong methodological consistency in mineral discrimination using ASTER VNIR+SWIR data. It should be noted that this agreement reflects internal algorithmic robustness rather than independent geological validation. Geological reliability is instead supported by documented field observations, lithological map comparisons, and spectral correspondence with the USGS spectral library. Validation employed documented field observations, lithological maps, and the USGS spectral library. Results reveal distinct spatial distributions of hematite-limonite/goethite, jarosite, kaolinite/smectite-illite-pyrophyllite-alunite, muscovite, hydrous silica/sericite/jarosite/hematite, epidote/chlorite, and calcite, closely associated with lithological units and unconsolidated deposits in Taylor, Wright, Victoria, and McKelvey Valleys. An inter-algorithm consistency check achieved 78.83% overall accuracy with a Kappa coefficient of 0.75, underscoring the robustness of ASTER VNIR+SWIR data for Antarctic mineral discrimination despite localized spectral mixing. Beyond refining the geological understanding of the McMurdo DVs, these results establish ASTER as an effective tool for regional mineralogical mapping in inaccessible polar terrains. The findings further strengthen the role of the Dry Valleys as a terrestrial analog for Mars, where similar mineralogical assemblages and spectral ambiguities have been observed, thereby contributing to both Antarctic geoscience and planetary exploration frameworks.
- Research Article
- 10.1103/9byv-ndvs
- Feb 6, 2026
- Physical Review Research
- Anonymous
We develop a theoretical framework to elucidate the mechanics and morphogenesis of open vesicles coupled to boundary filaments, capturing their geometric, energetic, and mechanical interplay. Using a spherical harmonics parametrization and constrained energy minimization, we systematically explore equilibrium morphologies as functions of filament length, stiffness, and topology, as well as membrane spontaneous curvature, uncovering a rich spectrum of shapes and transitions. For open vesicles bounded by flexible closed filaments, increasing filament length or spontaneous curvature drives transitions from cuplike to stomatocyte and budded morphologies, both axisymmetric and nonaxisymmetric, with continuous and discontinuous regimes mapped in a phase diagram. For open vesicles partially bounded by open filaments, the coupled filament-membrane system exhibits more complex morphological evolution, including free edge stretching or contraction, localized filament bending, and opening expansion with increasing filament length. The derived force and moment balances at the vesicle edge connect local geometric quantities, such as filament and membrane curvatures, to filament internal forces and membrane tension, providing a direct mechanical interpretation of shape equilibria. Our results reveal how filament geometry, topology, and bending stiffness govern membrane shape transformations and establish a general mechanical framework for coupled filament-membrane systems, such as DNA-vesicle complexes and other filament-mediated membrane structures.
- Research Article
- 10.1109/jstars.2026.3678308
- Jan 1, 2026
- IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
- Shaoquan Zhang + 7 more
Hyperspectral blind unmixing serves as a key technique in remote sensing image processing. Its core value lies in the ability to extract endmember spectral signatures and invert abundance fractions from mixed pixels without relying on prior endmember information. However, in practical applications, prevalent noise contamination in hyperspectral data often leads to degraded signal-to-noise ratio (SNR), which gives rise to spectral distortion and diminished image quality, consequently imposing a fundamental limitation on the accuracy of spectral unmixing. To overcome these challenges, this study introduces an innovative unmixing algorithm under the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula>-NMF framework that integrates endmember smoothness constraints with spatial abundance regularization based on Constrained Energy Minimization (CEM). Specifically, a non-smooth matrix is incorporated to enforce strong sparsity on endmembers, simultaneously smoothing image noise and improving endmember estimation accuracy. Furthermore, a novel dual-weight sparse regularization term is constructed by combining a CEM detector with a spatial weight, which concurrently enhances both the sparse representation and spatial continuity of abundance maps. On synthetic and real hyperspectral datasets, the proposed EISNMF algorithm yields greater accuracy in estimating both endmembers and abundances compared to existing blind unmixing techniques, proving to be particularly robust against high levels of noise.
- Research Article
2
- 10.3390/rs17162756
- Aug 8, 2025
- Remote Sensing
- Robin Gerster + 1 more
Target detection is a cornerstone task in hyperspectral image processing but faces significant challenges due to domain gaps. While statistical detectors like Constrained Energy Minimization (CEM) and Adaptive Cosine Estimator (ACE) are not prone to learned biases, in practice they still suffer from mismatches between the reference target spectrum and the spectral characteristics of the target in the test scene. We propose Test-time Adaptive Spectrum Refinement (TASR), a novel framework addressing this problem. TASR operates in an interpretable, lightweight, data-efficient manner, requiring only a single labeled source image of the target material. At test time, TASR dynamically refines the target spectrum to better align with the spectral properties of the test scene. This adaptive refinement enables detectors to effectively handle data with spectral variations, bridging the gap between the source and test spectra. To validate TASR, we conduct extensive experiments on established benchmarks and introduce a new dataset—ShadySunnyDiffuse (SSD)—which explicitly tests detector robustness to naturally occurring illumination changes. We further demonstrate the method’s versatility by applying it to camouflage detection and show compatibility with multiple statistical detectors. Our results establish TASR as a state-of-the-art approach in domain-adaptive hyperspectral target detection and target spectrum management.
- Research Article
- 10.3390/rs17132148
- Jun 23, 2025
- Remote Sensing
- Lei Wang + 2 more
The clever eye (CE) algorithm has been introduced for target detection in remote sensing image processing. It originally proposes the concept of data origin and can achieve the lowest average output energy compared to both the classical constrained energy minimization (CEM) and matched filter (MF) methods. In addition, it has been theoretically proven that the solutions of the best data origins can be attributed to solving a linear equation, which makes it computationally efficient. However, CE is only designed for single-target detection cases, while multiple-target detection is more demanding in real applications. In this paper, by naturally extending CE to a multiple-target case, we propose a unified algorithm termed multi-target clever eye (MTCE). The theoretical results in CE prompt us to consider an interesting question: do the MTCE solutions also share a similar structure to those of CE? Aiming to answer this question, we investigate a class of unconstrained non-convex optimization problems, where both the CE and MTCE models serve as special cases, which, interestingly, can also be utilized to solve a more generalized linear system. In addition, we further prove that all these solutions are globally optimal. In this sense, the analytical solutions of this generalized model can be deduced. Therefore, a unified framework is provided to deal with such a non-convex optimization problem, where both the solutions of MTCE and CE can be succinctly derived. Furthermore, its computational complexity is of the same magnitude as that of the other multiple-target-based methods. Experiments on both simulations and real hyperspectral remote sensing data verify our theoretical conclusions, and the comparison of quantitative metrics also demonstrates the advantage of our proposed MTCE method in multiple-target detection.
- Research Article
1
- 10.3390/diagnostics15121499
- Jun 12, 2025
- Diagnostics (Basel, Switzerland)
- Si-Wa Chan + 9 more
Background/Objectives: This research presents a novel analytical method for breast tumor characterization and tissue classification by leveraging intravoxel incoherent motion diffusion-weighted imaging (IVIM-DWI) combined with hyperspectral imaging techniques and deep learning. Traditionally, dynamic contrast-enhanced MRI (DCE-MRI) is employed for breast tumor diagnosis, but it involves gadolinium-based contrast agents, which carry potential health risks. IVIM imaging extends conventional diffusion-weighted imaging (DWI) by explicitly separating the signal decay into components representing true molecular diffusion (D) and microcirculation of capillary blood (pseudo-diffusion or D*). This separation allows for a more comprehensive, non-invasive assessment of tissue characteristics without the need for contrast agents, thereby offering a safer alternative for breast cancer diagnosis. The primary purpose of this study was to evaluate different methods for breast tumor characterization using IVIM-DWI data treated as hyperspectral image stacks. Dice similarity coefficients and Jaccard indices were specifically used to evaluate the spatial segmentation accuracy of tumor boundaries, confirmed by experienced physicians on dynamic contrast-enhanced MRI (DCE-MRI), emphasizing detailed tumor characterization rather than binary diagnosis of cancer. Methods: The data source for this study consisted of breast MRI scans obtained from 22 patients diagnosed with mass-type breast cancer, resulting in 22 distinct mass tumor cases analyzed. MR images were acquired using a 3T MRI system (Discovery MR750 3.0 Tesla, GE Healthcare, Chicago, IL, USA) with axial IVIM sequences and a bipolar pulsed gradient spin echo sequence. Multiple b-values ranging from 0 to 2500 s/mm2 were utilized, specifically thirteen original b-values (0, 15, 30, 45, 60, 100, 200, 400, 600, 1000, 1500, 2000, and 2500 s/mm2), with the last four b-value images replicated once for a total of 17 bands used in the analysis. The methodology involved several steps: acquisition of multi-b-value IVIM-DWI images, image pre-processing, including correction for motion and intensity inhomogeneity, treating the multi-b-value data as hyperspectral image stacks, applying hyperspectral techniques like band expansion, and evaluating three tumor detection methods: kernel-based constrained energy minimization (KCEM), iterative KCEM (I-KCEM), and deep neural networks (DNNs). The comparisons were assessed by evaluating the similarity of the detection results from each method to ground truth tumor areas, which were manually drawn on DCE-MRI images and confirmed by experienced physicians. Similarity was quantitatively measured using the Dice similarity coefficient and the Jaccard index. Additionally, the performance of the detectors was evaluated using 3D-ROC analysis and its derived criteria (AUCOD, AUCTD, AUCBS, AUCTD-BS, AUCODP, AUCSNPR). Results: The findings objectively demonstrated that the DNN method achieved superior performance in breast tumor detection compared to KCEM and I-KCEM. Specifically, the DNN yielded a Dice similarity coefficient of 86.56% and a Jaccard index of 76.30%, whereas KCEM achieved 78.49% (Dice) and 64.60% (Jaccard), and I-KCEM achieved 78.55% (Dice) and 61.37% (Jaccard). Evaluation using 3D-ROC analysis also indicated that the DNN was the best detector based on metrics like target detection rate and overall effectiveness. The DNN model further exhibited the capability to identify tumor heterogeneity, differentiating high- and low-cellularity regions. Quantitative parameters, including apparent diffusion coefficient (ADC), pure diffusion coefficient (D), pseudo-diffusion coefficient (D*), and perfusion fraction (PF), were calculated and analyzed, providing insights into the diffusion characteristics of different breast tissues. Analysis of signal intensity decay curves generated from these parameters further illustrated distinct diffusion patterns and confirmed that high cellularity tumor regions showed greater water molecule confinement compared to low cellularity regions. Conclusions: This study highlights the potential of combining IVIM-DWI, hyperspectral imaging techniques, and deep learning as a robust, safe, and effective non-invasive diagnostic tool for breast cancer, offering a valuable alternative to contrast-enhanced methods by providing detailed information about tissue microstructure and heterogeneity without the need for contrast agents.
- Research Article
2
- 10.2478/arsa-2025-0002
- Apr 1, 2025
- Artificial Satellites
- Amine Jellouli + 4 more
ABSTRACT The copper belt of Anti-Atlas is recognized with several mineral occurrences of Cu, Zn, Mn, Ag, Au, and iron. We used ASTER and OLI in lithological and mineral detection and mapping. The lithological mapping was performed using principal components analysis (PCA), minimum noise fraction (MNF), and two classifiers: maximum likelihood (ML) and support vector machine (SVM). The hydrothermally altered zones were detected based on ASTER VNIR/SWIR bands by the integration of Ninomiya indices and constrained energy minimization (CEM) algorithm. In our study area, the enhanced band combinations of ASTER MNF1, PC4, and PC2 and OLI MNF1, PC5, and PC3 were applied for lithological discrimination. The OLI and ML classification shows the best lithological mapping accuracy with an overall accuracy of 91.74% and a 0.90 Kappa coefficient, followed by SVM with an overall accuracy of 88.82% and a 0.86 Kappa coefficient using the same sensor. The hydrothermal alteration mapping reveals alunite, chlorite, calcite, epidote, illite, kaolinite, montmorillonite, muscovite, and pyrophyllite minerals, principally in phyllic and argillic altered areas. The adopted methodology for lithological and mineralogical mapping can be used in other regions with similar criteria to the study area.
- Research Article
4
- 10.1117/1.jbo.30.2.023518
- Feb 25, 2025
- Journal of biomedical optics
- Hsian-Min Chen + 4 more
We used three-dimensionally printed experimental molds and designed lard (lipid)-collagen mixed phantoms to simulate biological tissues to verify the practicality and accuracy of short-wave infrared (SWIR) hyperspectral imaging (HSI; 900 to 1700nm), subpixel target detection (STD), and linear spectral unmixing (LSU). We provide a foundation for future development, validation, and reproducibility of hyperspectral image-processing techniques. We aim to verify the use of SWIR HSI in bionic tissue phantoms. Second, we focus on the accuracy of STD and spectral unmixing techniques in hyperspectral image processing. Finally, the penetration ability of the technology and its applications at various depths and concentrations are explored. All experiments were conducted using an SWIR (900 to 1700nm) HSI sensor. Collagen phantoms of different thicknesses were created to test the penetration abilities. Lard (lipid) was embedded at different depths in the phantoms for STD, whereas LSU was performed on phantoms with varying collagen concentrations. The methods used included constrained energy minimization to detect the lard target and fully constrained least squares (FCLS) to estimate the abundance of collagen phantoms. SWIR HSI effectively penetrated the collagen phantoms. Specifically, STD techniques can accurately detect the presence of lard (lipids) at depths of 7 to 20mm in the collagen phantoms. Even at a depth of 68mm, the detection accuracy was 0.907. Moreover, in the LSU analysis, the FCLS method accurately estimated the abundance of collagen phantoms at different concentrations, with a correlation coefficient of 0.9917, indicating high accuracy across different concentrations. This study demonstrated that SWIR HSI is highly accurate for deep target detection and LSU. This technology has great potential for use in future noninvasive biomedical diagnostic models. Collagen phantoms are valuable tools for validating HSI algorithms and provide a solid foundation for clinical applications.
- Research Article
3
- 10.1109/tgrs.2024.3511953
- Jan 1, 2025
- IEEE Transactions on Geoscience and Remote Sensing
- Chein-I Chang + 3 more
Hyperspectral image classification (HSIC) has received considerable interest in recent years where most techniques are developed to classify images with background (BKG) removed by ground truth (GT). Unfortunately, in real scenarios, obtaining complete BKG knowledge is generally infeasible. Accordingly, HSIC performed with no BKG (HSIC-NB) is not realistic. Most importantly, many techniques claim to work well for HSIC-NB but perform poorly with BKG included. This article investigates issues arising from BKG in HSIC and further presents a new approach to HSIC with BKG (HSIC-B), called one class detection (OCD), which is based on the well-known hyperspectral subpixel detection technique, constrained energy minimization (CEM). In order for OCD to perform multiclass classification, OCD is further extended to hierarchical OCD (HOC) which is particularly designed to classify multiple classes in a hierarchical tree where each layer uses an iterative kernel CEM (IKCEM) or an iterative kernel target-constrained interference-minimized filter (IKTCIMF) to detect one class at a time for classification. Since M classes are classified by OCD in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M} -1$ </tex-math></inline-formula> layers in a hierarchical tree, a new concept of class classification priority (CCP) derived from CEM is specifically designed to rank all the classes along the tree in a prioritized order according to their CCP scores. The experimental results demonstrate that hierarchical OCD (HOCD) works well and performs significantly better than many existing HSIC-NB methods at the expense of slightly reduced classification accuracy compared to HSIC-N methods.
- Research Article
- 10.1051/m2an/2024065
- Jan 1, 2025
- ESAIM: Mathematical Modelling and Numerical Analysis
- Hywel Normington + 1 more
We consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations averaging the spins of two sublattices. For the static setting, which requires the solution of a constrained energy minimization problem, we introduce a discretization based on first-order finite elements and prove its Γ-convergence. Then, we propose and analyze two iterative algorithms for the computation of low-energy stationary points. The algorithms are obtained from (semi-)implicit time discretizations of gradient flows of the energy. Finally, we extend the algorithms to the dynamic setting, which consists of a nonlinear system of two Landau–Lifshitz–Gilbert equations solved by the two fields, and we prove unconditional stability and convergence of the finite element approximations toward a weak solution of the problem. Numerical experiments assess the performance of the algorithms and demonstrate their applicability for the simulation of physical processes involving antiferromagnetic and ferrimagnetic materials.
- Research Article
4
- 10.1016/j.pce.2024.103749
- Dec 1, 2024
- Physics and Chemistry of the Earth
- Farrage M Khaleal + 5 more
Remote sensing analysis and geodynamic setting of magmatic spessartine-almandine-bearing leucogranites, Um Addebaa area, southeastern Desert, Egypt: Bulk rock and mineral chemistry
- Research Article
- 10.3390/e26110890
- Oct 22, 2024
- Entropy (Basel, Switzerland)
- Wouter W L Nuijten + 2 more
This paper presents GraphPPL.jl, a novel probabilistic programming language designed for graphical models. GraphPPL.jl uniquely represents probabilistic models as factor graphs. A notable feature of GraphPPL.jl is its model nesting capability, which facilitates the creation of modular graphical models and significantly simplifies the development of large (hierarchical) graphical models. Furthermore, GraphPPL.jl offers a plugin system to incorporate inference-specific information into the graph, allowing integration with various well-known inference engines. To demonstrate this, GraphPPL.jl includes a flexible plugin to define a Constrained Bethe Free Energy minimization process, also known as variational inference. In particular, the Constrained Bethe Free Energy defined by GraphPPL.jl serves as a potential inference framework for numerous well-known inference backends, making it a versatile tool for diverse applications. This paper details the design and implementation of GraphPPL.jl, highlighting its power, expressiveness, and user-friendliness. It also emphasizes the clear separation between model definition and inference while providing developers with extensibility and customization options. This establishes GraphPPL.jl as a high-level user interface language that allows users to create complex graphical models without being burdened with the complexity of inference while allowing backend developers to easily adopt GraphPPL.jl as their frontend language.
- Research Article
4
- 10.3390/s24206713
- Oct 18, 2024
- Sensors
- Raana Esmaeeli + 3 more
Human activity recognition is known as the backbone of the development of interactive systems, such as computer games. This process is usually performed by either vision-based or depth sensors. So far, various solutions have been developed for this purpose; however, all the challenges of this process have not been completely resolved. In this paper, a solution based on pattern recognition has been developed for labeling and scoring physical exercises performed in front of the Kinect sensor. Extracting the features from human skeletal joints and then generating relative descriptors among them is the first step of our method. This has led to quantification of the meaningful relationships between different parts of the skeletal joints during exercise performance. In this method, the discriminating descriptors of each exercise motion are used to identify the adaptive kernels of the Constrained Energy Minimization method as a target detector operator. The results indicated an accuracy of 95.9% in the labeling process of physical exercise motions. Scoring the exercise motions was the second step after the labeling process, in which a geometric method was used to interpolate numerical quantities extracted from descriptor vectors to transform into semantic scores. The results demonstrated the scoring process coincided with the scores derived by the sports coach by a 99.5 grade in the R2 index.
- Research Article
11
- 10.1016/j.gexplo.2024.107598
- Oct 9, 2024
- Journal of Geochemical Exploration
- Mohamed A Abdelkader + 7 more
Fusing multi-source (remote sensing and geophysical) data and diverse approaches validation in targeting hydrothermal alteration and structural anomalies enhances the potential for accurately detecting and characterizing mineralization zones. Sentinel 2 data and ASTER were processed for lithological and hydrothermal alteration mapping in the rare metal-rich Umm Naggat area (Egypt). Different image processing techniques were implemented, including false color composites, minimum noise fraction, band rationing, band math, mineral indices, relative absorption band depth, and constrained energy minimization. The rare metal-bearing Umm Naggat younger granite (NYG) pluton was lithologically discriminated and intra-differentiated to mafic-rich biotite granites, mafic-poor alkali feldspar granites, and albitized granites. Extensive hydrothermal alterations, such as albitization, ferrugination, propylitization, argillization, and phyllitization, overprint the NYG pluton. Normalized standard deviation, automatic lineament extractions, and trend analysis highlighted the key structural directions (NW, NNW, NNE, and NE) and distinguished the NYG pluton as a moderate to high structural density zone. The high structural density and intensive alteration zones are spatially associated and more localized within the NYG pluton than the surrounding rocks. Spatial overlay analysis confirmed that the hydrothermal alterations and fluid circulation systems are structurally-controlled. Furthermore, the hydrothermal alteration mapping and structural analysis outcomes were verified by combining fieldwork, slab polishing, petrographic investigations, and mineral chemistry through semi-quantitative scanning electron microscopy with energy dispersive spectroscopy (SEM-EDS) and quantitative electron probe microanalysis (EPMA) analysis. As a result, the hydrothermal genesis of rare metal-bearing minerals (Nb-rutile, Nb-ilmenite, and columbite) close to or incorporated within alteration minerals (chlorite, muscovite, and hematite) is confirmed from the alteration zones (propylitic, phyllic, and ferruginated). In addition, biotite muscovitization and chloritization significantly contribute to the secondary rare metal enrichment. The current study emphasizes the extensive distribution of secondary rare metal-bearing minerals within the entire NYG pluton (not only limited to the northern albitized granite as depicted by previous studies), which might shed light on these hydrothermally-altered younger granites as a new potential source for Nb and Ta in Egypt.
- Research Article
4
- 10.3389/fmars.2024.1452737
- Oct 2, 2024
- Frontiers in Marine Science
- Song Zhao + 5 more
Timely and accurate monitoring of typical coastal targets using remote sensing technology is crucial for maintaining marine ecological stability. Hyperspectral target detection technology proves to be an effective tool in extracting various typical materials along the coastline. Traditional target detection methods using spectral domain information can effectively retain the intrinsic properties of the material. However, it is difficult to effectively recognize targets in homogeneous regions by using only spectral domain information, which may lead to insufficient utilization of spatial information. In this study, a detector based on signal-to-noise ratio fusion constrained energy minimization with low-rank sparse decomposition (SFLRSD) is proposed. This detector improves the separability of background and target by obtaining spatial domain information from hyperspectral images and fusing spectral domain information. First, total variation regularization and fractional Fourier transform are applied to process spatial and spectral domain information, respectively. The constrained energy minimization (CEM) detector is used to improve the separability between the target and background of the processed data. Then, the background and anomalies are represented as low-rank and sparse components, respectively, using low-rank sparse matrix factorization. This transforms the model solution into a covariance matrix problem, which is then solved using marginal distance difference (MDD) to isolate anomalous parts. Subsequently, the anomaly parts are fused with CEM detector results, weighted by their respective signal-to-noise ratios. This detection model leverages unified hyperspectral image features, enhancing spectral discreteness of anomalous targets and backgrounds. Finally, experiments on custom created hyperspectral dataset show that the proposed method outperforms other baseline methods in terms of visualization and quantitative performance. In this paper, we not only propose a new hyperspectral target detection method, but we also collect three typical marine litter of different materials by means of airborne hyperspectral remote sensing and construct four hyperspectral datasets in a real environment. All the simulation experiments in this paper are conducted in these four datasets.
- Research Article
- 10.1016/j.optcom.2024.131057
- Sep 1, 2024
- Optics Communications
- Zhiqiang Ning + 7 more
Joint spatial constrained energy minimization for gas identification in hyperspectral imaging
- Research Article
8
- 10.1007/s10915-024-02612-3
- Aug 13, 2024
- Journal of Scientific Computing
- R Altmann + 2 more
This paper is devoted to the numerical solution of constrained energy minimization problems arising in computational physics and chemistry such as the Gross–Pitaevskii and Kohn–Sham models. In particular, we introduce Riemannian Newton methods on the infinite-dimensional Stiefel and Grassmann manifolds. We study the geometry of these two manifolds, its impact on the Newton algorithms, and present expressions of the Riemannian Hessians in the infinite-dimensional setting, which are suitable for variational spatial discretizations. A series of numerical experiments illustrates the performance of the methods and demonstrates their supremacy compared to other well-established schemes such as the self-consistent field iteration and gradient descent schemes.
- Research Article
15
- 10.1038/s41598-024-68921-7
- Aug 6, 2024
- Scientific Reports
- Sobhi M Ghoneim + 4 more
Abu Marawat area in the Central Eastern Desert of Egypt is a very promising mineralization district located in the Golden Triangle area. The current study provides an integrated approach from multisource datasets including; remote sensing, airborne geophysical spectrometry and magnetic data supported by field studies and spectroscopic analyses for delineating potential mineralization localities. Several remote sensing techniques were adopted including; Band Ratios, Relative Band Depth, Mineralogical Indices, Spectral Angle Mapper, and Constrained Energy Minimization. These techniques showed that the alteration mineral assemblage is mainly, kaolinite, sericite, and iron oxides, with less abundant chlorite, epidote, and carbonates. In addition, the radiometry data were processed to map the localities with the highest possibility of potassic alteration abundance by integrating the potassium distribution, K/eTh ratio, and the F-parameter maps. The surface and subsurface linear structural features were also mapped using Digital Elevation Model (DEM) and aeromagnetic data, respectively. The surface linear structures were found exhibiting E-W and NE-SW trends, while, the subsurface structures showed dominant NW–SE trend. All the depicted fault trends match well with the local and regional geological and tectonic setting of the study area suggesting structural control on the mineralization in this area. Integration between the results obtained from both the remote sensing and the geophysical data was conducted by a GIS weighted overlay model. The obtained mineralization potentiality map highlights eight potential localities for mineralization. The accuracy of the adopted methodology was demonstrated through fieldwork and spectral analyses; several alteration indicators were observed, including quartz veins, iron oxides, kaolinite, malachite, montmorillonite, chlorite, talc, and sericite alteration indicator minerals. The adopted remote sensing-geophysical approach showed being very effective for mapping the hydrothermal gold-related alteration zones, and is recommended for other similar investigations.
- Research Article
1
- 10.19111/bulletinofmre.1518855
- Jul 18, 2024
- Bulletin Of The Mineral Research and Exploration
- Firdevs Güzel + 1 more
Palu segment is a part of the Eastern Anatolian Fault Zone (EAFZ), the most important active left-lateral strike-slip fault system in Turkey, and there are different mineral alterations in this zone. In the study, the spatial relationship between tectonic activity and mineral alterations was tested with the Getis-Ord Gi* statistic in and around Palu segment. Mineral alterations at the pixel level were determined from ASTER images by Ratio, Relative Band Depth (RBD), Mineral Indices, CROSTA, Constrained Energy Minimization (CEM), Mixed Tuned Matched Filter (MTMF) methods. According to the results, the spatial distribution of alteration minerals extending parallel to tectonically active fault lines and/or partially bounded by faults in the area. RBD, Mineral Indices, CROSTA, CEM, and MTMF image processing algorithms applied in the study gave consistent results in the spatial determination and mapping of hydrothermal alterations in the study area. At 99% and 95% confidence intervals, statistically significant cold spot clusters indicate the proximity of alterations to faults concentrated around fault lines. This degree of clustering of mineral alterations indicates regions with high alteration rates close to fault lines and areas with tectonic activity along fault lines.
- Research Article
5
- 10.1007/s43994-024-00158-6
- May 23, 2024
- Journal of Umm Al-Qura University for Applied Sciences
- Assran Sayed Mohamed Assran + 6 more
Remote sensing (RS) and airborne gamma-ray spectrometric (AGS) methods are utilized to delineate significant uranium zones and altered mineralization areas in Gabal Umm Tinassib and its surrounding region, situated in the northern section of the Egyptian Eastern Desert. AGS serves as a valuable tool for mapping surface geology and conducting mineral exploration. It assesses the concentrations of radioactive elements such as potassium (K), equivalent uranium (eU), and equivalent thorium (eTh). The concentration of radioelements exhibits measurable and significant variation according to lithology. On the other hand, several processing steps are employed for the RS data to generate high-quality images for geological mapping and to identify the mineralized alteration zones. The analysis of RS and AGS data in this study led to insightful conclusions. The utilization of False Color Composite (FCC) with the three best bands derived from the Optimum Index Factor (OIF), Principal Component Analysis (PCA) to extract two highly informative datasets, and the application of two band ratios contributed to accurate geological mapping. These band ratios notably identified identical alteration locations on both younger and older granite basement rocks. Additionally, the constrained energy minimization (CEM) technique effectively pinpointed alterations across these strata. The statistical analysis of AGS data revealed that radioactivity levels in the region range from 1.3 to 19.3 Ur for the total-count (TC), 0.2–3.6% for K, 0.09–11.6 ppm for eU, and 1.1–30.0 ppm for eTh. The estimated coefficient of variability (CoV) demonstrated that the three radio-elements exhibited normal distribution patterns across different rock units, with CoV values of less than 100%, except for K in the Malha Formation. High radiometric readings are observed in the outcroppings of younger and older granites. However, the lowest readings are recorded over undifferentiated Upper-Cretaceous sediments, Abu Rimth Formation, Galala Formation, and some parts of Quaternary sediments. The derived ternary radio-elements map highlights significant radiometric and related uranium anomalous zones as bright white regions. A strong correlation was found between high radiometric anomalous zones and the presumed occurrence of alteration zones in the study area.