Detection of nonlinear mixtures using Gaussian processes: Application to hyperspectral imaging

This paper studies a pixel by pixel nonlinearity detector for hyperspectral image analysis. The reflectances of linearly mixed pixels are assumed to be a linear combination of known pure spectral components (endmembers) contaminated by additive white Gaussian noise. Nonlinear mixing, however, is not restricted to any prescribed nonlinear mixing model. The mixing coefficients (abundances) satisfy the physically motivated sum-to-one and positivity constraints. The proposed detection strategy considers the distance between an observed pixel and the hyperplane spanned by the endmembers to decide whether that pixel satisfies the linear mixing model (null hypothesis) or results from a more general nonlinear mixture (alternative hypothesis). The distribution of this distance is derived under the two hypotheses. Closed-form expressions are then obtained for the probabilities of false alarm and detection as functions of the test threshold. The proposed detector is compared to another nonlinearity detector recently investigated in the literature through simulations using synthetic data. It is also applied to a real hyperspectral image.

Hyperspectral imaging captures detailed spectral data for remote sensing. However, due to the limited spatial resolution of hyperspectral sensors, each pixel of a hyperspectral image (HSI) may contain information from multiple materials. Although the hyperspectral unmixing (HU) process involves estimating endmembers, identifying pure spectral components, and estimating pixel abundances, existing algorithms mostly focus on just one or two tasks. Blind source separation (BSS) based on nonnegative matrix factorization (NMF) algorithms identify endmembers and their abundances at each pixel of HSI simultaneously. Although they perform well, the factorization results are unstable, require high computational costs, and are difficult to interpret from the original HSI. CUR matrix decomposition selects specific columns and rows from a dataset to represent it as a product of three small submatrices, resulting in interpretable low-rank factorization. In this paper, we propose a new blind HU framework based on CUR factorization called CUR-HU that performs the entire HU process by exploiting the low-rank structure of given HSIs. CUR-HU incorporates several techniques to perform the HU process with a performance comparable to state-of-the-art methods but with higher computational efficiency. We adopt a deterministic sampling method to select the most informative pixels and spectrum components in HSIs. We use an incremental QR decomposition method to reduce computation complexity and estimate the number of endmembers. Various experiments on synthetic and real HSIs are conducted to evaluate the performance of CUR-HU. CUR-HU performs comparably to state-of-the-art methods for estimating the number of endmembers and abundance maps, but it outperforms other methods for estimating the endmembers and the computational efficiency. It has a 9.4 to 249.5 times speedup over different methods for different real HSIs.

The class of Gaussian stochastic processes plays an important role in stochastic modeling and is widely used as a rich source of models in many areas of applied probability, including actuarial and financial mathematics. There are many practical and theoretical reasons for using Gaussian processes to model actuarial problems. For instance, the family of Gaussian processes covers a large class of correlation structures and enables explicit analysis of models for which classical renewal‐type tools do not work. On the other hand, theoretical results, mostly based on central limit theorem‐type argumentation, formally justify the use of Gaussian processes.

Due to the multidimensional nature of the hyperspectral image (HSI), multi-way arrays (called tensor) are one of the possible solutions for analyzing such data. In tensor algebra, CANDECOMP/PARAFAC decomposition (CPD) is a popular tool which has been successfully applied for the HSI data processing. However, on the one hand, CPD requires large memory for temporal variables. As a result, the memory usually overflows during the process for a real HSI whose size is large. On the other hand, so far no finite algorithm can well-determine the rank of the tensor to be decomposed. An inappropriate number of the rank may over-fit/under-fit the information provided by the tensor. To deal with these problems, this paper proposes an improved CPD with spectral and spatial partitioning for the HSI anomaly detection. First, the original HSI is divided into a set of smaller-sized sub-tensors. Second, CPD is applied onto each sub-tensor. Then, an anomaly detection algorithm is implemented and the detection results are fused along the spectral direction. Experiments with a real HSI data set reveals that the proposed method outperforms the CPD with no partition and the traditional RX anomaly detector with better detection performance.

Hyperspectral unmixing is the procedure by which the end component elements are calculated and their fractional abundances are found in each pixel in hyperspectral images. Sometimes several types of sound harm a hyperspectral photo. In a general scenario that takes mixed noise into consideration, this study addresses the hyperspectral non-mixing problem. Gaussian and sparse noises are expressly taken into account in the unmixing model. The problem of unmixing was formulated to use the combined shortage of abundance maps. For the modelling of flatness diagrams, a complete variation-based regularisation has also been used. For the solution of an algorithm for the optimization problem, the split-Bregman technique was used. The advantages of the method proposed are revealed by detailed preliminary findings on both real and synthetic images.

<p>Hyperspectral remote sensors collect image data for a large number of narrow, adjacent spectral bands. Every pixel in hyperspectral image involves a continuous spectrum that is used to classify the objects with great detail and precision. This paper presents hyperspectral image classification mechanism using genetic algorithm with empirical mode decomposition and image fusion used in preprocessing stage. 2-D Empirical mode decomposition method is used to remove any noisy components in each band of the hyperspectral data. After filtering, image fusion is performed on the hyperspectral bands to selectively merge the maximum possible features from the source images to form a single image. This fused image is classified using genetic algorithm. Different indices, such as K-means (KMI), Davies-Bouldin Index (DBI), and Xie-Beni Index (XBI) are used as objective functions. This method increases classification accuracy of hyperspectral image.</p>

Color is a key indicator for evaluating the quality of tea during processing; various processing procedures can significantly affect the content of fat-soluble pigments of tea, which in turn affects the color and quality of finished tea. Therefore, there is an urgent demand for the fast, non-destructive detection of pigments of stacked tea during processing. This paper presents the use of hyperspectral imaging technology (HSI), combined with machine learning algorithms, to detect chlorophyll a, chlorophyll b, and carotenoids in stacked matcha tea during processing. Firstly, a quantitative relationship between HSI data of tea and their pigment contents was developed based on regression analysis, and the results showed that exceptional prediction performance was achieved by the partial least squares regression (PLSR) algorithm combined with the feature band algorithm of competitive adaptive reweighting (CARS), and the Rp2 values of detection models of chlorophyll a, chlorophyll b and carotenoids were 0.90465, 0.92068 and 0.62666, respectively. Then, these quantitative detection models were extended to each pixel in hyperspectral images, achieving point-by-point prediction of pigment components, so the distribution of pigments of stacked tea leaves during processing procedures was successfully visualized on the processing line in situ. By integrating a hyperspectral imaging system into the real-world environment, operators can monitor pigment levels in real time and thus dynamically adjust processing parameters based on real-time data. This study enhances pigment detection efficiency in tea processing, supports process optimization, and aids in quality control.

Hyperspectral imaging is concerned with the measurement, analysis, and interpretation of spectra acquired from a given scene (or specific object) at a short, medium or long distance by an airbone or satellite sensor. Over the last few years, hyperspectral image data sets have been collected for a great amount of locations over the world, using a variety of instruments for Earth observation. Despite the increasing importance of hyperspectral images in remote sensing applications, there is no common repository of hyperspectral data intended to distribute and share hyperspectral data sets in the community. Quite opposite, the hyperspectral data sets which are available for public use are spread among different storage locations and present significant heterogeneity regarding the storage format, associated meta-data (if any), or ground-truth availability. As a result, the development of a standardized hyperspectral data repository is a highly desired goal in the remote sensing community. In this paper, we take a necessary first step towards the development of a digital repository for remotely sensed hyperspectral data. The proposed system allows uploading new hyperspectral data sets along with meta-data, ground-truth and analysis results, with the ultimate goal of sharing publicly available hyperspectral images within the remote sensing community. The database has been designed in order to allow storing relevant information for the hyperspectral data available through the system, including basic image characteristics (width, height, number of bands, format) and more advanced meta-data (ground-truth information, publications in which the data has been used). The current implementation consists of a front-end to ease the management of images through a web interface, thus containing both synthetic and real hyperspectral images from two highly representative instruments, such as NASAs Airborne Visible Infra-Red Imaging Spectrometer (AVIRIS) over the Cuprite Mining District in Nevada. Most importantly, the developed system includes a spectral unmixing-based content based image retrieval (CBIR) functionality which allows searching for images on the spectral unmixing information (spectrally pure components or endmembers and their associated abundances in the scene). This information is stored as meta-data associated to each hyperspectral image instance, and then used to search and retrieve images based on information content. This paper presents the design of the system and a preliminary validation of the unmixing-based retrieval functionality using both synthetic and real hyperspectral images stored in the database.

Unsupervised hyperspectral noise estimation and restoration via interband-invariant representation learning

As the interaction of light with the Earth surface is very complex, spectral reflectances are composed of nonlinear mixtures of the observed materials. Nonlinear mixing models have the disadvantage that not all spectra of a hyperspectral dataset necessarily follow the same particular mixing model. Moreover, most models lack a proper interpretation of the estimated parameters in terms of fractional abundances. In this paper, we present a semi-supervised nonlinear unmixing technique that overcomes these problems. In a first step, we apply a kernelized simplex volume maximization to select an overcomplete set of endmembers that precisely describe the hyperspectral data manifold. In a second step, this set is used as ground truth data in a supervised learning approach to generate fractional abundance maps from the entire dataset. For this, three methods are presented, based on kernelized sparse unmixing, feedforward neural networks, and gaussian processes. The proposed method is validated on simulated data, a dataset obtained by ray tracing, and a real hyperspectral image.

Hyperspectral image (HSI) denoising is an effective image processing technology to improve the quality of HSI. By exploiting the spectral-spatial characteristics of HSI, this paper proposes a HSI denoising method based on the Graph-structured Low Rank model and Non-Local constraint (GLRNL). Graph-structured low rank model can reveal the spectral similarity in HSI and preserve the distribution characteristics of spectral bands. The graph structure is used to ensure that the denoised HSI has similar spectral characteristics as the real HSI, and reduce the spectral distortions. Moreover, the non-local constraint in GLRNL adopts the spatial-spectral self-similarity and provides an effective side prior information for low rank calculation. Comparing with some traditional low rank and sparse model based HSI denoising methods, the proposed method achieves the competitive results on different simulated and real HSI data with various types of noise.

Image interpolation and denoising are important techniques in image processing. Recently, there has been a growing interest in the use of Gaussian processes (GP) regression for interpolation and denoising of image data. However, exact GP regression suffers from 0 (N 3 ) runtime for data size N, making it intractable for image data. Our GP-grid algorithm reduces the runtime complexity of GP from 0 (N 3 ) to 0 (N 3 1 2 ). We provide comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter. The GP interpolation method outperforms the commonly used bilinear interpolation method for polarimeters.

International audience

Longitudinal mental health assessments in mobile health (mHealth) settings are useful for monitoring subjects' mental health statuses but are often difficult to analyze because they generally appear on an ordinal scale and at unequal time intervals. In this article, we explore the use of Gaussian processes (GPs) and hierarchical modeling techniques to understand mental health trajectories based on repeated multi-item mHealth surveys on a Likert scale. We introduce the GP model for health trajectories, which is based on item response theory. In the study of trajectories, a subject's longitudinal collection of mHealth responses can be thought of as a single high-dimensional observation. We show how the GP is flexible enough to capture trends in individual trajectories even with the challenges associated with high-dimensional data. We also demonstrate how basis splines can be used to effectively capture nonlinear trends in the mean function of the GP. The high-dimension and ordinal nature of the data often make sampling from the posterior distribution in a Bayesian setting too slow to be practical. We show that using a Hilbert approximation for the GP trajectories can facilitate efficient sampling. We apply these methods to a longitudinal study that monitored college students' self-esteem.

A rapid and nondestructive method to determine the distribution map of protein, carbohydrate and sialic acid on Edible bird's nest by hyper-spectral imaging and chemometrics.