Linear Mixture Model Research Articles

A Simple Algorithm for Deriving an NDVI-Based Index Compatible between GEO and LEO Sensors: Capabilities and Limitations in Japan

Geostationary (GEO) satellite sensors provide earth observation data with a high temporal frequency and can complement low earth orbit (LEO) sensors in monitoring terrestrial vegetation. Consistency between GEO and LEO observation data is thus critical to the synergistic use of the sensors; however, mismatch between the sun–target–sensor viewing geometries in the middle-to-high latitude region and the sensor-specific spectral response functions (SRFs) introduce systematic errors into GEO–LEO products such as the Normalized Difference Vegetation Index (NDVI). If one can find a parameter in which the value is less influenced by geometric conditions and SRFs, it would be invaluable for the synergistic use of the multiple sensors. This study attempts to develop an algorithm to obtain such parameters (NDVI-based indices), which are equivalent to fraction of vegetation cover (FVC) computed from NDVI and endmember spectra. The algorithm was based on a linear mixture model (LMM) with automated computation of the parameters, i.e., endmember spectra. The algorithm was evaluated through inter-comparison between NDVI-based indices using off-nadir GEO observation data from the Himawari 8 Advanced Himawari Imager (AHI) and near-nadir LEO observation data from the Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) as a reference over land surfaces in Japan at middle latitudes. Results showed that scene-dependent biases between the NDVI-based indices of sensors were −0.0004±0.018 (mean ± standard deviation). Small biases were observed in areas in which the fractional abundances of vegetation were likely less sensitive to the view zenith angle. Agreement between the NDVI-based indices of the sensors was, in general, better than the agreement between the NDVI values. Importantly, the developed algorithm does not require regression analysis for reducing biases between the indices. The algorithm should assist in the development of algorithms for performing inter-sensor translations of vegetation indices using the NDVI-based index as a parameter.

Study on the Effect of Surface Roughness on the Spectral Unmixing of Mixed Pixels

In the spectrum measurement experiment, the roughness of the object surface is an essential factor that cannot be ignored. In this experiment, a group of mixed pixel samples with different mixing ratios were designed, and these samples were printed on four kinds of papers with different roughness. The spectral characteristics of mixed pixels with different roughness are quantitatively analyzed by using the measured spectral data. The linear spectral mixture model is used for spectral decomposition, and the effect of roughness on the unmixing precision of mixed pixels was studied. The surface roughness will affect the reflectivity of the mixed pixel. Specifically, the higher the roughness is, the higher the reflectivity of the sample is. This phenomenon is more noticeable when the proportion of white endmember (PWE) is large, and as the white area ratio decreases, the reflectance difference gradually decreases. When the surface roughness of the sample is less than 3.339 μm, the spectral decomposition is performed using a linear spectral mixing model in the visible light band. The average error of the unmixing is less than 0.53%, which is lower than the conventional standard spectral measurement error. In other words, when the surface roughness of the sample is controlled within a specific range, the effect of roughness on the unmixing accuracy of the mixed pixels is small, and this effect can be almost ignored. Multiple scattering within the pixels is the key to model selection and unmixing accuracy, when using the ASD FieldSpec3 spectrometer to perform spectral reflectance measurement and linear spectral unmixing experiments. If the surface roughness of the sample to be measured is less than the maximum wavelength of the spectrometer, the experimental results believe that the photon energy is mainly mirror reflection on the surface of the object and diffuse reflection. At this time, it is still a better choice to use a linear spectral mixing model to decompose the mixed pixels.

Approach of spectral information-based image registration similarity

For local intensity-based image registration methods, a template of a predefined size is adopted. Some measure of similarity between the images is used to determine when the optimal alignment has occurred. Most intensity-based similarity utilizes the statistical and spatial information of an image. However, there are significant nonlinear radiometric differences between infrared and visible data. Images of natural scenes usually do not have enough spatial features within the template. Hence, many similarities will be useless when dealing with infrared and visible data. Minor eigenvalues (ME) image registration similarity is presented with the exploitation the spectral properties of remote sensing images. ME similarity is based on the linear spectral mixture model and detects control points through searching the minimum of ME of the covariance matrix. Experiments on Landsat-7 satellite Enhanced Thematic Mapper Plus data are performed to verify and evaluate the effectiveness. Transformation performance curves, correct match ratio (CMR), and registration accuracy are also discussed. According to the data, root-mean-square error of phase correlations is 0.0722 pixels and the CMR of ME similarity is nearly 100%. The results on the basis of TM1, TM2, TM3, and TM4 band images indicate that the proposed similarity holds promise for infrared and color image registration in natural scenes, with advantages over previous normal mutual information and gradient mutual information similarities.

Learning the Clustering of Longitudinal Shape Data Sets into a Mixture of Independent or Branching Trajectories

Given repeated observations of several subjects over time, i.e. a longitudinal data set, this paper introduces a new model to learn a classification of the shapes progression in an unsupervised setting: we automatically cluster a longitudinal data set in different classes without labels. Our method learns for each cluster an average shape trajectory (or representative curve) and its variance in space and time. Representative trajectories are built as the combination of pieces of curves. This mixture model is flexible enough to handle independent trajectories for each cluster as well as fork and merge scenarios. The estimation of such non linear mixture models in high dimension is known to be difficult because of the trapping states effect that hampers the optimisation of cluster assignments during training. We address this issue by using a tempered version of the stochastic EM algorithm. Finally, we apply our algorithm on different data sets. First, synthetic data are used to show that a tempered scheme achieves better convergence. We then apply our method to different real data sets: 1D RECIST score used to monitor tumors growth, 3D facial expressions and meshes of the hippocampus. In particular, we show how the method can be used to test different scenarios of hip-pocampus atrophy in ageing by using an heteregenous population of normal ageing individuals and mild cog-nitive impaired subjects.

Spectral Mixture Model Inspired Network Architectures for Hyperspectral Unmixing

In many statistical hyperspectral unmixing approaches, the unmixing task is essentially an optimization problem given a defined linear or nonlinear spectral mixture model. However, most of the model inference algorithms require a time-consuming iterative procedure. On the other hand, neural networks have been recently used to estimate abundances given some training samples, or directly estimate endmembers and abundances simultaneously in an unsupervised setting. However, their disadvantages are clear: lack of interpretability and reliance on the large training set. Model-inspired neural networks are constructed by the problem model and its corresponding inference algorithm. It incorporates the prior knowledge of physical model and algorithm into network architecture, combining the advantages of model-based and learning-based methods. This article deeply unfolds the linear mixture model and the corresponding iterative shrinkage-thresholding algorithm (ISTA) to build two unmixing network architectures. The first assumes that the set of endmembers are known, and the deep unfolded ISTA model is only for abundance estimation; and the second is used for blind unmixing to estimate both endmembers and abundances at the same time. The networks can be trained by supervised and unsupervised schemes, respectively, with a small-size training set, and then, unmixing becomes a feedforward process, which is very fast since no iteration is required. The experimental results show their competitive performance compared with the state-of-the-art unmixing approaches.

CT scans in childhood predict subsequent brain cancer: Finite mixture modelling can help separate reverse causation scans from those that may be causal

BackgroundExcess brain cancers observed after computed tomography (CT) scans could be caused by ionizing radiation. However, as scans are often used to investigate symptoms of brain cancer, excess cancers could also be due to reverse causation bias. We used finite mixture models (FMM) to differentiate CT exposures that are plausibly causal from those due to reverse causation. MethodsPersons with at least one CT scan exposure and a subsequent diagnosis of brain cancer were selected from a cohort of 11 million young Australians. We fitted FMMs and used the posterior probability to inform the choice of exclusion periods. We validated our findings using a separate clinical dataset describing the time between first symptoms and brain cancer diagnosis (pre-diagnostic symptomatic interval; PSI). ResultsThe cohort included 1028 persons with a diagnosed brain tumor and exposed to a total of 1,450 CT scans. The best-fitting model was a generalized linear mixture model using the exponential distribution with three latent classes and two covariates (age at exposure and year of exposure). The 99th percentile classifier cutoff was 18.9 months. The sample-size weighted mean of the 99th percentile of the PSI, derived from clinical data, was 15.6 months. ConclusionsTo minimize reverse causation bias in studies of CT scan and brain cancer, the optimal exclusion period is one to two years (depending on the choice of classifier). This information will inform the interpretation of current and future studies.

Nonlocal Low-Rank Abundance Prior for Compressive Spectral Image Fusion

Compressive spectral imaging (SI) (CSI) acquires few random projections of an SI reducing acquisition, storage, and, in some cases, processing costs. Then, this acquisition framework has been widely used in various tasks, such as target detection, video processing, and fusion. Particularly, compressive spectral image fusion (CSIF) aims at obtaining a high spatial-spectral resolution SI from two sets of compressed measurements: one from a hyperspectral image with a high-spectral low-spatial resolution, and one from a multispectral image with high-spatial low-spectral resolution. Most of the literature approaches include prior information, such as global low rank, smoothness, and sparsity, to solve the resulting ill-posed CSIF inverse problem. More recently, the high self-similarities exhibited by SIs have been successfully used to improve the performance of CSI inverse problems, including a nonlocal low-rank (NLLR) prior. However, to the best of our knowledge, this NLLR prior has not been implemented in the solution of the CSIF inverse problem. Therefore, this article formulates an approach that jointly includes the global low rank, the smoothness, and the NLLR priors to solve the CSIF inverse problem. The global low-rank prior is introduced with the linear mixture model that describes the SI as a linear combination of a set of few end-members to specific abundances. In this article, either the end-members are accurately estimated from the compressed measurements or initialized from a fast reconstruction of the hyperspectral image. Also, it assumes that the abundances preserve the smoothness and NLLR priors of the SI so that the fused image is obtained from the end-members and abundances that result when minimizing a cost function including the sum of two data fidelity terms and two regularizations: the smoothness and the NLLR. Simulations over three data sets show that the proposed approach increases the CSIF performance compared with literature approaches.

Convolutional Autoencoder for Spectral–Spatial Hyperspectral Unmixing

Blind hyperspectral unmixing is the process of expressing the measured spectrum of a pixel as a combination of a set of spectral signatures called endmembers and simultaneously determining their fractional abundances in the pixel. Most unmixing methods are strictly spectral and do not exploit the spatial structure of hyperspectral images (HSIs). In this article, we present a new spectral-spatial linear mixture model and an associated estimation method based on a convolutional neural network autoencoder unmixing (CNNAEU). The CNNAEU technique exploits the spatial and the spectral structure of HSIs both for endmember and abundance map estimation. As it works directly with patches of HSIs and does not use any pooling or upsampling layers, the spatial structure is preserved throughout and abundance maps are obtained as feature maps of a hidden convolutional layer. We compared the CNNAEU method to four conventional and three deep learning state-of-the-art unmixing methods using four real HSIs. Experimental results show that the proposed CNNAEU technique performs particularly well and consistently when it comes to endmembers' extraction and outperforms all the comparison methods.

Efficiency of subspace-based estimators for elliptical symmetric distributions

Subspace-based algorithms that exploit the orthogonality between a sample subspace and a parameter-dependent subspace have proved very useful in many applications in signal processing. The purpose of this paper is to complement theoretical results already available on the asymptotic (in the number of measurements) performance of subspace-based estimators derived in the Gaussian context to real elliptical symmetric (RES), circular complex elliptical symmetric (C-CES) and non-circular CES (NC-CES) distributed observations in the same framework. First, the asymptotic distribution of M-estimates of the orthogonal projection matrix is derived from those of the M-estimates of the covariance matrix. This allows us to characterize the asymptotically minimum variance (AMV) estimator based on estimates of orthogonal projectors associated with different M-estimates of the covariance matrix. A closed-form expression is then given for the AMV bound on the parameter of interest characterized by the column subspace of the mixing matrix of general linear mixture models. We also specify the conditions under which the AMV bound based on Tyler’s M-estimate attains the stochastic Cramér-Rao bound (CRB) for the complex Student t and complex generalized Gaussian distributions. Finally, we prove that the AMV bound attains the stochastic CRB in the case of maximum likelihood (ML) M-estimate of the covariance matrix for RES, C-CES and NC-CES distributed observations, which is equal to the semiparametric CRB (SCRB) recently introduced.

Forest change detection based on sub-pixel tree cover estimates using Landsat-OLI and Sentinel 2 data

The paper presents a method of forest change detection and its application for clear-cutting and selective logging disturbances assessment. Based on optical remote sensing data it uses of satellite images and sub-pixel estimation of tree cover, performed by using linear spectral mixture model for estimation of forest area portion in each pixel. The paper describes the main steps of the change detection method and the influence of algorithm input settings on the results. The method was implemented as a satellite data processing tool and was tested on selected sites in Primorsky Krai and the Republic of Udmurtia regions. Forest change maps related to logging in year 2016 were developed over the test areas using the Landsat 8 and Sentinel-2 satellite data. The paper compares obtained change areas with official logging statistics and Global Forest Change project data in order to evaluate the method performance for clear-cutting and selective logging area detection.

Hyperspectral Shadow Removal via Nonlinear Unmixing

Removing shadows that are often present in remotely sensed hyperspectral images is important for both enhancing the interpretability of the data and further target analysis. Shadow removal approaches based on spectral unmixing have been proposed in the literature using the linear mixture model. However, objects that produce shadows may also introduce light scattering, and the higher order interactions of photons can cause nonlinearity. This letter integrates the nonlinear hyperperspectral unmixing into the unmixing-based shadow removal, and the effects of applying typical nonlinear algorithms within the approach are investigated. The usefulness of nonlinear unmixing in hyperspectral shadow removal is verified based on the results of applications to both laboratory-created real data and actual airborne data.

Spatiotemporal Patterns of Impervious Surface Area and Water Quality Response in the Fuxian Lake Watershed.

The increase of urbanization level has led to the rapid increase of impervious surface area (ISA). The aim of this work is to clarify the relationship between the ISA and water quality and lay a foundation for the improvement and protection of the water quality in the basin. Taking the Fuxian Lake Basin in Yunnan Province as an example, based on the Landsat ETM+ remote sensing image and the Gram–Schmidt (GS) image fusion algorithm, the four-terminal model and the linear spectral mixture model (LSMM) were used to extract the impervious surface of the watershed from 2006 to 2015. And statistical methods were used to distinguish its relationship with water quality. The results show that the four-terminal model and the linear spectral mixture model can effectively extract the impervious surface information of the Fuxian Lake Basin. The average root mean square error (RMS) of the image decomposition results from 2006 to 2015 was less than 0.02. In the past 10 years, the ISA has changed significantly in the Fuxian Lake Basin. The ISA showed an overall upward trend from 2006 to 2015. It increased from 24.73 km2 in 2006 to 35.14 km2 in 2015, an increase of 10.81 km2. From the value anomaly, the ISA in 2006 and 2009 is lower than the multiyear average, and those in the other years are higher than the multiyear average. The percentage of ISA in the basin was significantly positively correlated with Chemical Oxygen Demand-Mn (CODMn) and total phosphorus (TP) (r is 0.772, 0.763), and the correlation in the flooding season was greater than that in the dry season. The ISA threshold for water quality deterioration is around 10% in the Fuxian Lake Basin. Reducing ISA coverage, controlling ISA to less than 10%, and preventing nonpoint source pollution during flooding season will be the best measures to effectively improve the water quality environment in the basin.

Investment in social capital by the Korean elderly and baby-boomers

Abstract Social capital (SC) is both an input and an output of individuals’ economic choices, but relatively little is known about SC investment, particularly in individuals’ old age. With a premise that SC is an individual-level concept in which individuals purposely invest, we estimate elderly individuals’ stock and investment in SC using principal component analysis of their social engagement, networks, and trust in social institutions. We describe the distribution of the SC stock and investment across various demographic groups. Based on a capital-accumulation model, and using linear regressions and mixture models, we test hypotheses about the drivers – expected benefits, costs, depreciation, preexisting SC, and social-capital in one’s community – and trajectories of elderly individuals’ SC investment. Implications for their life satisfaction are also assessed. Using four waves of the Korean Longitudinal Study of Ageing, we find that the elderly exhibit gradual attrition of SC, but women retain more SC on account of better mental health and higher returns on investment from lower starting points. Expected returns on SC are associated positively with individuals’ investment, while the opportunity cost of one’s time and SC depreciation are associated weakly negatively with it. Physical and human capital are complementary to SC, encouraging investment. Community-level stock and investment in SC lead to higher investment by individuals themselves.

Estimating fractional vegetation cover from leaf area index and clumping index based on the gap probability theory

Gap probability theory provides a theoretical equation to calculate fractional vegetation cover (FVC). However, the main algorithms used in present FVC products generation are still the linear mixture model and machine learning methods. The reason to limit the gap probability theory applied in the product algorithm is the availability and accuracy of leaf area index (LAI) and clumping index (CI) products. With the improvement of the LAI and CI products, it is necessary to assess whether the algorithm based on gap probability theory using the present products can improve the accuracy of FVC products. In this study, we generated the FVC estimates based on the gap probability theory (FVCgap) with a resolution of 500 m every 8 days for Europe. FVCgap estimates were validated with field FVC measurements of ImagineS from 2013 to 2015 for crop types. Two existing FVC products, Geoland2 Version1 (GEOV1) and Multisource data Synergized Quantitative remote sensing production system (MuSyQ), were used to inter-compare with the FVCgap estimates. FVCgap estimates showed a better agreement with field FVC measurements, with lowest root mean square error (RMSE) (0.1211) and bias (0.0224), than GEOV1 and MuSyQ FVC products. The inter-annual and seasonal variations of FVCgap estimates were also showed the most consistent with field measurements.

Landscape changes in avulsive river systems: Case study of Taquari River on Brazilian Pantanal wetlands

The Pantanal is an important active sedimentary basin in central South America where highly diverse flora and fauna are sustained by seasonal floods. Intense land use in the catchment areas enhanced sediment load and destabilized avulsive river systems in the plains. A well-known avulsion in the Taquari River during the 1980–90s, called “Zé da Costa”, has shifted the river mouth and drastically changed the nearby landscapes, making them difficult to map because of the hard access and the large variations in spectral and spatial attributes of raster data like Landsat images. Therefore, we developed a useful method to map and explore landscape changes in “Zé da Costa” avulsion that combines geotagged field pictures, randomly selected high-resolution orbital truths, normalized difference vegetation index, digital elevation models, linear spectral mixture models and Landsat historical imagery in pixel-based and object-oriented supervised classifications. We found that bands in green, red, and near-infrared spectra provide better mapping results with object-oriented algorithms for deriving and studying temporal dry/wet ratio dynamics. The temporal analyses of the dry/wet ratio showed that avulsions in the Taquari River have the potential to change permanently the “Zé da Costa” area into a dry landscape, making it susceptible for land use (deforestation and fire), except areas seasonally inundated by the floods of the Paraguay River. Overall, our method might be also useful for long-term studies of land use and climate change in avulsive rivers in wetlands around the world.

Controlled Synthesis of Magnetic Iron Oxide Nanoparticles: Magnetite or Maghemite?

Today, magnetic nanoparticles are present in multiple medical and industrial applications. We take a closer look at the synthesis of magnetic iron oxide nanoparticles through the co-precipitation of iron salts in an alkaline environment. The variation of the synthesis parameters (ion concentration, temperature, stirring rate, reaction time and dosing rate) change the structure and diameter of the nanoparticles. Magnetic iron oxide nanoparticles are characterized by X-ray diffraction (XRD), Raman spectroscopy and transmission electron microscopy (TEM). Magnetic nanoparticles ranging from 5 to 16 nm in diameter were synthesized and their chemical structure was identified. Due to the evaluation of Raman spectra, TEM and XRD, the magnetite and maghemite nanoparticles can be observed and the proportion of phases and the particle size can be related to the synthesis conditions. We want to highlight the use of Raman active modes A1g of spinel structured iron oxides to determine the content of magnetite and maghemite in our samples. Magnetite nanoparticles can be derived from highly alkaline conditions even without establishing an inert atmosphere during the synthesis. The correlation between the particle properties and the various parameters of the synthesis was modelled with linear mixture models. The two models can predict the particle size and the oxidation state of the synthesized nanoparticles, respectively. The modeling of synthesis parameters not only helps to improve synthesis conditions for iron oxide nanoparticles but to understand crystallization of nanomaterials.

Análise da variabilidade da precipitação frente às mudanças no uso da terra no município de Tucuruí-PA

O objetivo do presente estudo foi analisar as variações da precipitação e a dinâmica espacial do uso e cobertura da terra no município de Tucuruí, Pará, Brasil, no período de 1980 a 2015. Para isso, foram utilizados dados das estações meteorológicas do Instituto Nacional de Meteorologia (INMET) e da Agência Nacional de Águas (ANA). Para o estudo da precipitação no município foram utilizados testes de Mann-Kendall e Sen's Slope com nível de significância de 95%. Para compreender as mudanças da cobertura da terra na área de estudo, utilizou-se o modelo linear de mistura em imagens Landsat-TM 3, 5 e 8 segmentadas, para análise multitemporal das classes da cobertura da terra identificadas no município. Os resultados indicaram que não houve tendências nas séries dos totais anuais de precipitação (1980 a 2015). Porém, constataram-se significativas variações do regime de chuvas interanuais, com precipitação média anual de 2431.6 mm. Os dados indicaram sazonalidade caraterizada por duas estações distintas: (1) menos chuvosa, entre os meses de junho a novembro; e (2) mais chuvosa, entre os meses de dezembro a maio. O mapeamento mostrou diferentes classes de uso da terra no período estudado, no entanto, as classes da vegetação nativa, vegetação secundária, hidrografia e solo exposto apresentaram variação espaço-temporal não linear. Contudo, a classe do solo exposto exibiu um comportamento crescente desde 1980, com o início das obras da usina hidrelétrica. Em relação à precipitação anual do município, nota-se que não há relação direta com as classes do uso e cobertura da terra nos anos analisados.

Speaker Feature Modeling Utilizing Constrained Maximum Likelihood Linear Regression and Gaussian Mixture Models

Speaker Feature Modeling Utilizing Constrained Maximum Likelihood Linear Regression and Gaussian Mixture Models

Generating High Resolution LAI Based on a Modified FSDAF Model

Leaf area index (LAI) is an important parameter for monitoring the physical and biological processes of vegetation canopy. Due to the constraints of cloud contamination, snowfall, and instrument conditions, most of the current satellite remote sensing LAI products have lower resolution that cannot satisfy the needs of vegetation remote sensing application in areas of high heterogeneity. We proposed a new model to generate high resolution LAI, by combining linear pixel unmixing and the Flexible Spatiotemporal Data Fusion (FSDAF) method. This method derived the input data of FSDAF by downscaling the MODIS (Moderate Resolution Imaging Spectroradiometer) data with a linear spectral mixture model. Through the improved input parameters of the algorithm, the fusion of MODIS LAI and LAI at Landsat spatial resolution estimated by Support Vector Regression model was realized. The fusion accuracy of generated LAI data was validated based on Sentinel-2 LAI products. The results showed that strong correlation between predicted LAI and Sentinel-2 LAI in sample sites was observed with higher correlation coefficients and lower Root Mean Square Error. Compared to the simulation results of FSDAF, the modified FSDAF model showed higher accuracy and reflected more spatial details in the boundary areas of different land cover types.

Learning Nonlinear Mixtures: Identifiability and Algorithm

Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is well-studied, under frameworks such as independent component analysis and constrained matrix factorization. Nevertheless, when the linear mixtures are distorted by an unknown nonlinear functions -- which is well-motivated and more realistic in many cases -- the identifiability issues are much less studied. This work proposes an identification criterion for a nonlinear mixture model that is well grounded in many real-world applications, and offers identifiability guarantees. A practical implementation based on a judiciously designed neural network is proposed to realize the criterion, and an effective learning algorithm is proposed. Numerical results on synthetic and real-data corroborate effectiveness of the proposed method.