Spectral Subset Research Articles

Integration of PRISMA Hyperspectral Satellite Data with Ground Based Geological investigation for Mapping alteration minerals associated with the Neem-Ka-Thana Cu belt in Rajasthan, India

Hydrothermal deposits are commonly associated with specific alteration minerals that serve as key indicators for mineral exploration. The Neem Ka Thana Cu Belt, situated southeast of the Khetri Cu deposit within the Alwar-Ajabgarh sub-basin of the North Delhi Fold Belt, is notable for its Bornite-rich Cu-S mineralization. Despite its geological significance, detailed spectral mapping to delineate the alteration minerals associated with base metal mineralisation remained limited. This study addresses this gap by utilizing the “PRecursore IperSpettrale della Missione Applicativa” (PRISMA) hyperspectral sensor to detect and map alteration minerals associated with Cu-S mineralization.To achieve this, we applied Relative Band Depth (RBD) indices on targeted spectral subsets of PRISMA data to identify Fe-oxides/hydroxides and Al-OH-bearing minerals. We detected key alteration minerals, including muscovite, illite, chlorite, montmorillonite and Fe-oxide and hydroxides such as goethite, hematite, and limonite, by targeting their diagnostic absorption features. The resulting spectral maps highlighting the spatial distribution of the targeted mineral groups were validated with field investigations and laboratory assessments. The study demonstrates that the integration of hyperspectral analysis with conventional geological techniques can help to understand the mineral distribution and associated alteration processes. The use of PRISMA hyperspectral data provides a powerful, non-invasive means for reconnaissance mapping of exposed lithologies, delivering targeted information that is crucial for optimizing subsequent field investigations and drilling operations. The present work highlights the potential of PRISMA data in advancing the methodologies of mineral exploration and lithological mapping, contributing valuable insights for the geoscientific community.

Estimation of LAI of tobacco plant using selected spectral subsets of visible and near-infrared reflectance spectroscopy

Flue-cured tobacco is a main economic crop, and leaves are the direct product of tobacco plant. Monitoring leaf area index (LAI) of tobacco plant is important to field management, yield prediction, and industry regulation. Hyperspectral data have hundreds of narrow spectral bands in continuous spectral ranges, significantly advancing monitoring of LAI. However, considering spectral responses of LAI vary with wavelength, the use of the full spectral range in estimation of LAI is redundant. To reduce spectral redundancy and improve estimation of LAI, spectral subsets were selected based on importance of spectral bands. Variable importance in the projection (VIP) score obtained by partial least squares regression (PLSR) was adopted to measure the importance. The study was conducted in Yunnan Province, China. Canopy reflectance spectra of tobacco plant were measured in two consecutive growth seasons. Genetic algorithm (GA) and PLSR were used for model calibration. The identified important spectral regions for estimation of LAI were red edge, near-infrared (NIR), and green regions. In estimation of LAI of tobacco plant, compared with the estimation using the full spectral range of VNIR reflectance spectra, normalized root mean square error (NRMSE) and coefficient of determination (R2) values were improved from 10.30% and 0.83 to 7.68% and 0.90 and from 18.78% and 0.43 to 7.65% and 0.90 by using the reflectance spectra in identified spectral regions in the growth seasons in 2021 and 2022 separately. In addition to the identified continuous spectral regions, central bands of the identified spectral regions also achieved estimation of LAI, with the highest R2 value reaching 0.72. The selected spectral subsets improved estimation accuracy and reduced model complexity. The results indicate that selected spectral subsets are effective and promising in estimation of LAI, providing an alternative for estimation of LAI using hyperspectral data.

Estimation of soil organic carbon content by Vis-NIR spectroscopy combining feature selection algorithm and local regression method

ABSTRACT Soil organic carbon (SOC) content is a critical parameter for evaluating soil health. However, high redundancy and invalid information in soil hyperspectral data can reduce the accuracy and stability of SOC prediction models. This study developed a global partial least squares regression (PLSR) model and a local PLSR model for agricultural soils in the LUCAS 2015 database. Some variable selection methods were combined with the regression models and their effects on prediction accuracy were explored. In addition, when the genetic algorithm is utilized for spectral feature selection, we obtained a more representative spectral subset through a novel coding approach. The results illustrated that the best SOC estimation accuracy was achieved by the local PLSR combined with a coding-improved genetic algorithm (GA), with R 2 of 0.71, RMSEP of 5.7 g kg -1 , and RPD of 1.87. This study demonstrates that appropriate spectral band selection only slightly enhances the model performance of both global and local regressions, as PLSR models using the full spectrum show similar performance. Local PLSR models consistently outperform global ones using full spectrum or variable selection algorithms.

Identifying cancer risks using spectral subset feature selection based on multi-layer perception neural network for premature treatment

Recently, human beings have been affected mainly by dreadful cancer diseases. Predicting cancer risk levels is a major challenge in biomedical research for feature selection and classification at the margins. To resolve this problem, we propose a Subset Clustering-Based Feature Selection using a Multi-Layer Perception Neural Network (SCFS-MLPNN). Initially, pre-processing is carried out with Intensive Mutual Disease Influence Rate (IMDIR) to identify the relational features. In addition, the Successive Disease Pattern Stimulus Rate (SDPSR) is carried out to create relative feature patterns. Based on the patterns, the features are selected and grouped into clustering. Inter-Class Sub-Space Clustering (ICSSC) is applied to split the features by class labels depending on the marginal rate. From the class labels, marginal features are obtained using spectral subset feature selection (SSFS). The selected features are then trained in a Multi-Layer Perception Neural Network (MLPNN) classifier to classify the patient features by risk. Its contribution is to exploit subset features to improve classification accuracy by clustering relational features. The proposed classifier yields higher classification accuracy than previous methods and observes cancer detection for early detection. Therefore, the proposed method achieved a risk analysis accuracy of 91.8% and an F-measure of 91.3% for early detection, which is recommended for early diagnosis.

Multispectral Characteristics of Glacier Surface Facies (Chandra-Bhaga Basin, Himalaya, and Ny-Ålesund, Svalbard) through Investigations of Pixel and Object-Based Mapping Using Variable Processing Routines

Fundamental image processing methods, such as atmospheric corrections and pansharpening, influence the signal of the pixel. This morphs the spectral signature of target features causing a change in both the final spectra and the way different mapping methods may assign thematic classes. In the current study, we aim to identify the variations induced by popular image processing methods in the spectral reflectance and final thematic maps of facies. To this end, we have tested three different atmospheric corrections: (a) Quick Atmospheric Correction (QUAC), (b) Dark Object Subtraction (DOS), and (c) Fast Line-of-Sight Atmospheric Analysis of Hypercubes (FLAASH), and two pansharpening methods: (a) Hyperspherical Color Sharpening (HCS) and (b) Gram–Schmidt (GS). WorldView-2 and WorldView-3 satellite images over Chandra-Bhaga Basin, Himalaya, and Ny-Ålesund, Svalbard are tested via spectral subsets in traditional (BGRN1), unconventional (CYRN2), visible to near-infrared (VNIR), and the complete available spectrum (VNIR_SWIR). Thematic mapping was comparatively performed using 12 pixel-based (PBIA) algorithms and 3 object-based (GEOBIA) rule sets. Thus, we test the impact of varying image processing routines, effectiveness of specific spectral bands, utility of PBIA, and versatility of GEOBIA for mapping facies. Our findings suggest that the image processing routines exert an extreme impact on the end spectral reflectance. DOS delivers the most reliable performance (overall accuracy = 0.64) averaged across all processing schemes. GEOBIA delivers much higher accuracy when the QUAC correction is employed and if the image is enhanced by GS pansharpening (overall accuracy = 0.79). SWIR bands have not enhanced the classification results and VNIR band combination yields superior performance (overall accuracy = 0.59). The maximum likelihood classifier (PBIA) delivers consistent and reliable performance (overall accuracy = 0.61) across all processing schemes and can be used after DOS correction without pansharpening, as it deteriorates spectral information. GEOBIA appears to be robust against modulations in atmospheric corrections but is enhanced by pansharpening. When utilizing GEOBIA, we find that a combination of spatial and spectral object features (rule set 3) delivers the best performance (overall accuracy = 0.86), rather than relying only on spectral (rule set 1) or spatial (rule set 2) object features. The multiresolution segmentation parameters used here may be transferable to other very high resolution (VHR) VNIR mapping of facies as it yielded consistent objects across all processing schemes.

Evaluation of artificial neural network performance for classification of potato plants infected with potato virus Y using spectral data on multiple varieties and genotypes

Potato virus Y (Potyviridae, PVY) is a plant virus that poses a significant threat to potato producers on a global basis. The pathogen has disrupted seed potato supplies and negatively impacted yield and quality of commercial potato crops. The potato industry currently manages PVY infection levels via insecticide applications, regional seed certification programs that rely on field scouting to visually assess individual plants for infection status, and destructive and costly tissue sampling coupled with laboratory assays. Despite these efforts, PVY continues to confound potato industry stakeholders resulting in economic harm. Remote sensing and machine learning provide for the development of new tools to more accurately detect and spatially quantify PVY-infected plants versus the current state of the art. However, there is a need to understand how the occurrence of many different potato varieties impact the dynamics of developing models to detect potato plants impacted with PVY and their potential effectiveness. This study evaluates classification modelling outcomes using spectral datasets collected in different temporal and spatial environments (greenhouse and a production field) on multiple potato varieties consisting of labelled instances of plants infected with PVY and those not infected with the virus. A modelling framework was developed to support iterative modelling runs using artificial neural network (ANN) architectures configured as binary classifiers to develop sample populations to support statistical analysis on model performance using specific spectral subsets. When using spectral data to detect PVY-infected plants, ANN models achieved the highest mean accuracy of 0.894 on a single variety. Conversely, the same ANN model architecture only achieved a mean accuracy of 0.575 on a spectral data set representing 29 potato breeding lines. Additionally, statistical analysis indicates spectral regions including the red edge, near infrared and shortwave infrared contain more important spectral features for the ANN classifier introduced in this research.

A spectral grouping-based deep learning model for haze removal of hyperspectral images

Haze contamination is a common issue in optical remote sensing images, including hyperspectral images (HSIs), which can distort the spectral features of land cover objects. Over the last decades, although many haze removal solutions have been developed, very few studies have focused on haze removal of HSIs. Moreover, most of these methods cannot fully explore the abundant spectral information of HSIs in haze removal. To cope with the issues, a data driven method is proposed for haze removal of HSIs in this paper. Specifically, we design a spectral grouping network (SG-Net) to fully utilize the useful information in each spectral band during the reconstruction. To facilitate the relationship construction between hazy image and the corresponding haze-clear image, the proposed SG-Net first groups each HSI into several spectral subsets based on the intra-spectral correlations. Then, these subsets are convoluted in parallel with multiple branches for feature extraction. Furthermore, a novel attention block is designed to connect the adjacent branches for feature transmission, which can distill the useful information (e.g., uncontaminated information in longer wavelength bands) of each subset and assist the reconstruction of HSIs. Comprehensive experiments on both simulated and real haze HSIs showed that SG-Net is more accurate than seven state-of-the-art haze removal methods and is also more robust to different haze levels and shapes.

Identification of informative spectral ranges for predicting major chemical constituents in corn using NIR spectroscopy

Many studies have been conducted using NIR spectroscopy to predict corn constituents; however, a systematic investigation of the spectral sub-regions under the scope of overtones and combinations has not been performed. In this study, the corn spectra were divided into second overtones (1100–1388 nm), first overtones (1390–1852 nm), and combinations (1852–2498 nm). Then, using variable importance in projection and genetic algorithm, each region was inspected sequentially to identify the most informative sub-region for each attribute to improve interpretability. The identified spectral subsets were further tuned to select the most influential bands for each attribute. The sub-regions in combinations bands was most informative for predicting water (1908–2108 nm, 2 bands), oil (2176–2304 nm, 6 bands), and protein (2130–2190 nm, 3 bands), whereas the first overtones region was the best for predicting starch (1452–1770 nm, 5 bands). Results provided valuable information for potential hardware and software improvements.

Performance of hyperspectral data in predicting and mapping zinc concentration in soil

Reflectance spectroscopy in visible, near-infrared, and short-wave infrared (VNIR-SWIR) region has been recognized as a promising alternative for prediction of heavy metal concentration in soil. Compared with VNIR-SWIR reflectance spectroscopy, VNIR reflectance spectroscopy is less affected by atmospheric water vapor and has relatively high signal to noise ratio. The performances of VNIR and VNIR-SWIR hyperspectral data in predicting and mapping heavy metal concentration in soil were explored. In this study, laboratory spectra of soil samples collected from an agricultural area and Advanced Hyperspectral Imaging (AHSI) remote sensing imagery were used to predict and map zinc (Zn) concentration with genetic algorithm and partial least squares regression (GA-PLSR). The entire spectral regions of VNIR-SWIR and VNIR and spectral subsets extracted from the entire spectral regions were used in the prediction. For the laboratory spectra, the combination of the spectral bands extracted from the absorption features at 500 nm and in 600–800 nm obtained the highest prediction accuracy with the root mean square error (RMSE) and coefficient of determination (R2) values of 8.90 mg kg−1 and 0.72. For soil spectra from AHSI remote sensing imagery, the highest prediction accuracy was achieved by using the spectral bands extracted from the absorption feature in 600–800 nm with the RMSE and R2 values of 9.02 mg kg−1 and 0.75. Soil Zn concentration maps were generated with the established prediction models using AHSI remote sensing imagery. Analysis on the Zn concentration maps shows that the prediction model established using the spectral bands extracted from the absorption feature in 600–800 nm has a better performance in mapping Zn concentration. The results indicate that VNIR hyperspectral data outperforms VNIR-SWIR hyperspectral data in predicting and mapping Zn concentration in soil, which provides an alternative to the application of hyperspectral data in soil science.

Estimation of soil organic matter content using selected spectral subset of hyperspectral data

Soil organic matter (SOM) content plays an important role in the global carbon cycle and agricultural activities. Reflectance spectroscopy has been recognized as a promising method to rapidly estimate SOM content. However, the existing estimation methods mainly apply partial least squares regression (PLSR) to the entire spectral region of hyperspectral data. Here we proposed a method to extract the informative spectral subset based on spectral characteristics of soil constituents, which was then used to estimate SOM content with PLSR. Genetic algorithm (GA) and variable importance in the projection (VIP) score of PLSR were adopted to further select spectral bands separately. Both laboratory spectra of soil samples collected from an agricultural area and a hyperspectral satellite image were used to evaluate the performance of the method. For the estimations of SOM content using laboratory spectra, compared with the estimation using the entire spectral region of 400–2400 nm, the model accuracy was improved by using the spectral bands associated with clay minerals and the combined spectral bands of organic matter and clay minerals. For the estimations using soil spectra from hyperspectral remote sensing image, the RMSE and R2 values were improved from 0.91% and 0.34 to 0.55% and 0.76 by using the spectral bands associated with organic matter in comparison with the entire spectral region of 390–1029 nm. The estimation model developed with GA-PLSR using soil spectra from the hyperspectral satellite image was applied to map SOM content. Results suggest that estimating SOM content using informative spectral subset is promising and can be transferred to the hyperspectral satellite image to map SOM content.

Estimating Soil Properties and Nutrients by Visible and Infrared Diffuse Reflectance Spectroscopy to Characterize Vineyards

Visible, near, and shortwave infrared (VIS-NIR-SWIR) reflectance spectroscopy, a cost-effective and rapid means of characterizing soils, was used to predict soil sample properties for four vineyards (central and north-western Spain). Sieved and air-dried samples were measured using a portable spectroradiometer (350–2500 nm) and compared for pistol grip (PG) versus contact probe (CP) setups. Raw data processed using standard normal variate (SVN) and detrending transformation (DT) were grouped into four subsets (VIS: 350–700 nm; NIR: 701–1000 nm; SWIR: 1001–2500 nm; and full range: 350–2500 nm) in order to identify the most suitable range for determining soil characteristics. The performance of partial least squares regression (PLSR) models in predicting soil properties from reflectance spectra was evaluated by cross-validation. The four spectral subsets and transformed reflectances for each setup were used as PLSR predictor variables. The best performing PLSR models were obtained for pH, electrical conductivity, and phosphorous (R2 values above 0.92), while models for sand, nitrogen, and potassium showed moderately good performances (R2 values between 0.69 and 0.77). The SWIR subset and SVN + DT processing yielded the best PLSR models for both the PG and CP setups. VIS-NIR-SWIR reflectance spectroscopy shows promise as a technique for characterizing vineyard soils for precision viticulture purposes. Further studies will be carried out to corroborate our findings.

Analysing spectroscopy data using two-step group penalized partial least squares regression

A statistical challenge to analyse hyperspectral data is the multicollinearity between spectral bands. Partial least squares (PLS) has been extensively used as a dimensionality reduction technique through constructing lower dimensional latent variables from the spectral bands that correlate with the response variables. However, it does not take into account the grouping structure of the full spectrum where spectral subsets may exhibit distinct relationships with the response variables. We propose a two-step group penalized PLS regression approach by performing a PLS regression on each group of predictors identified from a clustering approach in the first step. In the second step, a group penalty is imposed on the latent components to select the group with the highest predictive power. Our proposed method demonstrated a superior prediction performance, higher R-squared value and faster computation time over other PLS variations when applied to simulations and a real-world observational data set. Interpretations of the model performance are illustrated using the real-world data example of leaf spectra to indirectly quantify leaf traits. The method is implemented in an R package called “groupPLS”, which is accessible from github.com/jialiwang1211/groupPLS.

A two-step iterative algorithm for sparse hyperspectral unmixing via total variation

Sparse hyperspectral unmixing is a hot topic in the field of remote sensing. Its goal is to find an optimal spectral subset, from a large spectral library, to properly model the mixed pixels in hyperspectral images. Sparse unmixing via variable splitting augmented Lagrangian and total variation (SUnSAL-TV) incorporates a TV regularizer into sparse unmixing, achieving a promising unmixing performance. Note that, SUnSAL-TV is solved by the framework of the alternating direction method of multipliers (ADMM). In this paper, we first propose a weighted collaborative sparse unmixing via TV model, named as WCSU-TV, for hyperspectral unmixing. Then a two-step iterative strategy, based on ADMM, is designed to solve the proposed model. Its key idea is to compute the current solution by a linear combination of the results of two previous iterates, instead of only using current solution in classic ADMM. Experiments on simulated and real hyperspectral data illustrate the effectiveness of the proposed approach.

Potential of hyperspectral AVIRIS-NG data for vegetation characterization, species spectral separability, and mapping

The present study deals with hyperspectral species mapping, utilization of optimal bands, and studying the spectral separability of vegetation species using AVIRIS-NG data. To reduce data redundancy, a wide range of optimal spectral bands (491 nm, 541 nm, 641 nm, 722 nm, 772 nm, 852 nm, 942 nm, 1047 nm, 1132 nm, 1443 nm, and 2475 nm) were selected and simulated for classification using artificial neural network (ANN) and support vector machine (SVM) techniques. Band-to-band correlative plots demonstrated huge data redundancy (correlation as high as R2 = 0.99, at 682 nm and 687 nm) owing to the need of spectral sub-setting. ANN classification exhibited dominance of low-elevation (0–800 m) evergreen forest (44.81%) followed by Tectona grandis plantation (25.97%). Mid-elevation (800–1450) evergreen forest contributes ~ 16.79% of area, and primarily consists of Coffee arabica (3.14%) and Camelia sinensis (0.7%). Spectrally, each vegetation species exhibited distinct spectral characteristics plotted against different wavelengths and unveiled unique spectral signatures and their classification provided comparable accuracy in species identification in ANN (86.45%) as well as in SVM (86.75%). With immense potential and applicability, spectroscopic AVIRIS-NG data is highly recommended for characterizing, quantifying, modeling, and mapping vegetation.

Bandwise Model Based on Spectral Prior Information for Sparse Unmixing

The purpose of sparse unmixing (SU) is to find the optimal spectral subset from the spectral library and uses this subset to model each pixel in the hyperspectral data. The existing SU methods concern Gaussian noise a lot and focus less on the varied intensity of Gaussian noise in different bands and other types of noise, e.g., impulse noise and deadlines. Besides, the high coherence of the spectral library limits the performance of SU. Given the aforementioned problems, this article proposes a new method, called bandwise model based on spectral prior information (BMSPI). This proposed BMSPI models the Gaussian noise across different spectral bands and the other types of mixed noise under the maximum a posteriori probability framework, and decreases the effect of high coherence in the spectral library with the spectral prior information. The alternating direction method of multipliers is adopted to solve the BMSPI. The results of the simulated and real data experiments show that the bandwise model can suppress noises of different types effectively, and the spectral prior information is conducive to guide SU. The advantage of BMSPI is that the mentioned information is used completely. Thus, the accuracy of abundance estimation is improved.

Mapping leaf area index in a mixed temperate forest using Fenix airborne hyperspectral data and Gaussian processes regression

Machine learning algorithms, in particular, kernel-based machine learning methods such as Gaussian processes regression (GPR) have shown to be promising alternatives to traditional empirical methods for retrieving vegetation parameters from remotely sensed data. However, the performance of GPR in predicting forest biophysical parameters has hardly been examined using full-spectrum airborne hyperspectral data. The main objective of this study was to evaluate the potential of GPR to estimate forest leaf area index (LAI) using airborne hyperspectral data. To achieve this, field measurements of LAI were collected in the Bavarian Forest National Park (BFNP), Germany, concurrent with the acquisition of the Fenix airborne hyperspectral images (400−2500 nm) in July 2017. The performance of GPR was further compared with three commonly used empirical methods (i.e., narrowband vegetation indices (VIs), partial least square regression (PLSR), and artificial neural network (ANN)). The cross-validated coefficient of determination (Rcv2) and root mean square error (RMSEcv) between the retrieved and field-measured LAI were used to examine the accuracy of the respective methods. Our results showed that using the entire spectral data (400−2500 nm), GPR yielded the most accurate LAI estimation (Rcv2 = 0.67, RMSEcv = 0.53 m2 m−2) compared to the best performing narrowband VIs SAVI2 (Rcv2 = 0.54, RMSEcv = 0.63 m2 m−2), PLSR (Rcv2 = 0.74, RMSEcv = 0.73 m2 m−2) and ANN (Rcv2 = 0.68, RMSEcv = 0.54 m2 m−2). Consequently, when a spectral subset obtained from the analysis of VIs was used as model input, the predictive accuracies were generally improved (GPR RMSEcv = 0.52 m2 m−2; ANN RMSEcv = 0.55 m2 m−2; PLSR RMSEcv = 0.69 m2 m−2), indicating that extracting the most useful information from vast hyperspectral bands is crucial for improving model performance. In general, there was an agreement between measured and estimated LAI using different approaches (p > 0.05). The generated LAI map for BFNP using GPR and the spectral subset endorsed the LAI spatial distribution across the dominant forest classes (e.g., deciduous stands were generally associated with higher LAI values). The accompanying LAI uncertainty map generated by GPR shows that higher uncertainties were observed mainly in the regions with low LAI values (low vegetation cover) and forest areas which were not well represented in the collected sample plots. This study demonstrated the potential of GPR for estimating LAI in forest stands using airborne hyperspectral data. Owing to its capability to generate accurate predictions and associated uncertainty estimates, GPR is evaluated as a promising candidate for operational retrieval applications of vegetation traits.

Simultaneously Multiobjective Sparse Unmixing and Library Pruning for Hyperspectral Imagery

Sparse hyperspectral unmixing has attracted increasing investigations during the past decade. Recent research has indicated that library pruning algorithms can significantly improve the unmixing accuracies by reducing the mutual coherence of the spectral library. Inspired by the good performance of library pruning, in this article we propose a new hyperspectral unmixing algorithm which integrates the idea of library pruning and sparse representation. An obvious challenge for pruning algorithms is that the real endmembers must be preserved after pruning. Unfortunately, recent proposed pruning algorithms, such as multiple signal classification are actually prepruning strategies, which cannot guarantee that the endmembers exactly exist in the selected spectral subset when the image noise is strong. To overcome this difficulty, we develop a simultaneous optimization approach which involves the pruning operation into the optimization process. Compared with existing prepruning-based unmixing methods, the proposed algorithm can gradually compress the search space of sparse representation, which may relieve the loss of spectral information caused by the rapid compression of the library. Instead of simply designing a regularizer, in this article we utilize a multiobjective-based framework where reconstruction error, sparsity error, and the pruning projection function are considered as three parallel objectives, so as to avoid the manually settings of regularization parameters. Moreover, we have provided theoretical analysis and proof for the reasonability of our pruning objective. Experiments on synthetic hyperspectral data may indicate the superiority of the proposed method under high-noise conditions.

Kato S-Spectrum in the Quaternionic Setting

In a right quaternionic Hilbert space, for a bounded right linear operator, the Kato S-spectrum is introduced and studied to a certain extent. In particular, it is shown that the Kato S-spectrum is a non-empty compact subset of the S-spectrum and it contains the boundary of the S-spectrum. Using right-slice regular functions, local S-spectrum, at a point of a right quaternionic Hilbert space, and the local spectral subsets are introduced and studied. The S-surjectivity spectrum and its connections to the Kato S-spectrum, approximate S-point spectrum and local S-spectrum are investigated. The generalized Kato S-spectrum is introduced and it is shown that the generalized Kato S-spectrum is a compact subset of the S-spectrum.

Leaf Biochemistry Parameters Estimation of Vegetation Using the Appropriate Inversion Strategy.

Biochemistry parameters of vegetation are important indicators of the photosynthetic process and provide a substantial amount of data about the status of ecosystems. Estimation of these parameters are greatly affected by the correlations of spectral bands and the sensitivity of each biochemistry parameter to inversion models. Hence, reducing the spectral dimension and inefficient computation process using an appropriate inversion strategy is significant for biochemistry parameters’ estimation. In this work, we used band-selection-based artificial neural networks (ANNs) combined with feature weighting (FW) and principal component analysis (PCA) process to reduce the sensitive spectral correlations and to improve the inversion model predictability for four biochemistry parameters: chlorophyll a and b (Cab), carotenoid (Car), equivalent water thickness (EWT), and leaf mass per area (LMA). We analyzed the model performance by conducting different inversion strategies, including: (1) linking reflectance (R), transmittance (T), and R&T spectral properties in different numbers of band to four biochemistry parameters; (2) simultaneously and then separately inverting them using FW- and PCA-ANNs considering their sensitivity to the ANN model; and (3) choosing a spectral subset from R, T spectrum for EWT, and LMA inversion successively. The results show that: (i) the FW- and PCA-ANN models exhibit efficient improvements by selecting less spectral characteristics; (ii) concurrently inverting EWT and LMA can achieve a satisfactory R2, while it is inappropriate for Cab and Car whose optimal R2 are obtained by separately inverting all four biochemicals; (iii) the properties of R, T, and R&T spectra exhibit various performances on parameters inversion.

On the discrete Fuglede and Pompeiu problems

We investigate the discrete Fuglede's conjecture and Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric condition under which a multiset of a finite abelian group has the discrete Pompeiu property. Using this description and the revealed connection we prove that Fuglede's conjecture holds for $\mathbb{Z}_{p^n q^2}$, where $p$ and $q$ are different primes. In particular, we show that every spectral subset of $\mathbb{Z}_{p^n q^2}$ tiles the group. Further, using our combinatorial methods we give a simple proof for the statement that Fuglede's conjecture holds for $\mathbb{Z}_p^2$.