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Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as encapsulating the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance when dealing with hyperspectral image (HSI) analysis, but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample (OOS) data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the latent space (typically low) is linear. This is a particularly strong assumption, especially when dealing with HSIs due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on high-dimensional model representation (HDMR) is proposed, which enables a nonlinear embedding function to project OOS samples into the latent space. The proposed method is compared to manifold learning methods along with their linear counterparts and achieves promising performance in terms of classification accuracy for a representative set of HSIs. [ABSTRACT FROM AUTHOR]

Remote sensing observations, products, and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to analyze and understand the underlying physical dynamics and processes driving the Earth System. Dimensionality reduction methods can work with spatio-temporal data sets and decompose the information efficiently. Principal component analysis (PCA), also known as empirical orthogonal functions (EOFs) in geophysics, has been traditionally used to analyze climatic data. However, when nonlinear feature relations are present, PCA/EOF fails. In this article, we propose a nonlinear PCA method to deal with spatio-temporal Earth system data. The proposed method, called rotated complex kernel PCA (ROCK-PCA for short), works in reproducing kernel Hilbert spaces to account for nonlinear processes, operates in the complex kernel domain to account for both space and time features, and adds an extra rotation for improved flexibility. The result is an explicitly resolved spatio-temporal decomposition of the Earth data cube. The method is unsupervised and computationally very efficient. We illustrate its ability to uncover spatio-temporal patterns using synthetic experiments and real data. Results of the decomposition of three essential climate variables are shown: satellite-based global gross primary productivity (GPP), soil moisture (SM), and reanalysis sea surface temperature (SST) data. The ROCK-PCA method allows identifying their annual and seasonal oscillations, as well as their nonseasonal trends and spatial variability patterns. The main modes of variability of GPP and SM match expected distributions of land-cover and eco-hydrological zones, respectively; the interannual component of SM is shown to be highly correlated with El Niño Southern Oscillation (ENSO) phenomenon; and the SST annual oscillation is perfectly uncoupled in magnitude and phase from the global warming trend and ENSO anomalies, as well as from their mutual interactions. We provide the working source code of the presented method for the interested reader in https://github.com/DiegoBueso/ROCK-PCA. [ABSTRACT FROM AUTHOR]

In many remote sensing applications, one wants to estimate variables or parameters of interest from observations. When the target variable is available at a resolution that matches the remote sensing observations, standard algorithms, such as neural networks, random forests, or the Gaussian processes, are readily available to relate the two. However, we often encounter situations where the target variable is only available at the group level, i.e., collectively associated with a number of remotely sensed observations. This problem setting is known in statistics and machine learning as multiple instance learning (MIL) or distribution regression (DR). This article introduces a nonlinear (kernel-based) method for DR that solves the previous problems without making any assumption on the statistics of the grouped data. The presented formulation considers distribution embeddings in reproducing kernel Hilbert spaces and performs standard least squares regression with the empirical means therein. A flexible version to deal with multisource data of different dimensionality and sample sizes is also presented and evaluated. It allows working with the native spatial resolution of each sensor, avoiding the need for matchup procedures. Noting the large computational cost of the approach, we introduce an efficient version via random Fourier features to cope with millions of points and groups. Real experiments involve the Soil Moisture Active Passive (SMAP) vegetation optical depth (VOD) data for the estimation of crop production in the U.S. Corn Belt and the Moderate Resolution Imaging Spectroradiometer (MODIS) and Multi-angle Imaging SpectroRadiometer (MISR) reflectances for the estimation of aerosol optical depth (AOD). An exhaustive empirical evaluation of the method is done against naive (linear and nonlinear) approaches based on input-space means as well as previously presented methods for MIL. We provide source code of our methods in http://isp.uv.es/code/dr.html. [ABSTRACT FROM AUTHOR]

Anomalous change detection (ACD) is an important problem in remote sensing image processing. Detecting not only pervasive but also anomalous or extreme changes has many applications for which methodologies are available. This paper introduces a nonlinear extension of a full family of anomalous change detectors. In particular, we focus on algorithms that utilize Gaussian and elliptically contoured (EC) distribution and extend them to their nonlinear counterparts based on the theory of reproducing kernels’ Hilbert space. We illustrate the performance of the kernel methods introduced in both pervasive and ACD problems with real and simulated changes in multispectral and hyperspectral imagery with different resolutions (AVIRIS, Sentinel-2, WorldView-2, and Quickbird). A wide range of situations is studied in real examples, including droughts, wildfires, and urbanization. Excellent performance in terms of detection accuracy compared to linear formulations is achieved, resulting in improved detection accuracy and reduced false-alarm rates. Results also reveal that the EC assumption may be still valid in Hilbert spaces. We provide an implementation of the algorithms as well as a database of natural anomalous changes in real scenarios http://isp.uv.es/kacd.html. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the effect of spatial and spectral compression on the performance of statistically based retrieval. Although the quality of the information is not completely preserved during the coding process, experiments reveal that a certain amount of compression may yield a positive impact on the accuracy of retrievals. We unveil two strategies, both with interesting benefits: either to apply a very high compression, which still maintains the same retrieval performance as that obtained for uncompressed data; or to apply a moderate to high compression, which improves the performance. As a second contribution of this paper, we focus on the origins of these benefits. On the one hand, we show that a certain amount of noise is removed during the compression stage, which benefits the retrievals performance. On the other hand, we analyze the effect of compression on spectral/spatial regularization (smoothing). We quantify the amount of information shared among the spatial neighbors for the different methods and compression ratios. We also propose a simple strategy to specifically exploit spectral and spatial relations and find that, when these relations are taken into account beforehand, the benefits of compression are reduced. These experiments suggest that compression can be understood as an indirect way to regularize the data and exploit spatial neighbors information, which improves the performance of pixelwise statistics-based retrieval algorithms. [ABSTRACT FROM AUTHOR]

Establishing causal relations between random variables from observational data is perhaps the most important challenge in today’s science. In remote sensing and geosciences, this is of special relevance to better understand the earth’s system and the complex interactions between the governing processes. In this paper, we focus on an observational causal inference, and thus, we try to estimate the correct direction of causation using a finite set of empirical data. In addition, we focus on the more complex bivariate scenario that requires strong assumptions and no conditional independence tests can be used. In particular, we explore the framework of (nondeterministic) additive noise models, which relies on the principle of independence between the cause and the generating mechanism. A practical algorithmic instantiation of such principle only requires: 1) two regression models in the forward and backward directions and 2) the estimation of statistical independence between the obtained residuals and the observations. The direction leading to more independent residuals is decided to be the cause. We instead propose a criterion that uses the sensitivity (derivative) of the dependence estimator, the sensitivity criterion allows to identify samples most affecting the dependence measure, and hence, the criterion is robust to spurious detections. We illustrate the performance in a collection of 28 geoscience causal inference problems, a database of radiative transfer models simulations and machine learning emulators in vegetation parameter modeling involving 182 problems, and assessing the impact of different regression models in a carbon cycle problem. The criterion achieves the state-of-the-art detection rates in all cases, and it is generally robust to noise sources and distortions. The presented approach confirms the validity in observational bivariate problems in the earth sciences. [ABSTRACT FROM AUTHOR]

Physically based radiative transfer models (RTMs) are widely used in Earth observation to understand the radiation processes occurring on the Earth’s surface and their interactions with water, vegetation, and atmosphere. Through continuous improvements, RTMs have increased in accuracy and representativity of complex scenes at expenses of an increase in complexity and computation time, making them impractical in various remote sensing applications. To overcome this limitation, the common practice is to precompute large lookup tables (LUTs) for their later interpolation. To further reduce the RTM computation burden and the error in LUT interpolation, we have developed a method to automatically select the minimum and optimal set of input–output points (nodes) to be included in an LUT. We present the gradient-based automatic LUT generator algorithm (GALGA), which relies on the notion of an acquisition function that incorporates: 1) the Jacobian evaluation of an RTM and 2) the information about the multivariate distribution of the current nodes. We illustrate the capabilities of GALGA in the automatic construction and optimization of MODTRAN-based LUTs of different dimensions of the input variables space. Our results indicate that when compared with a pseudorandom homogeneous distribution of the LUT nodes, GALGA reduces: 1) the LUT size by >24%; 2) the computation time by ~27%; and 3) the maximum interpolation relative errors by at least 10%. It is concluded that an automatic LUT design might benefit from the methodology proposed in GALGA to reduce interpolation errors and computation time in computationally expensive RTMs. [ABSTRACT FROM AUTHOR]

Solving inverse problems is central in geosciences and remote sensing. The radiative transfer models (RTMs) represent mathematically the physical laws that rule the phenomena in remote sensing applications (forward models). The numerical inversion of the RTM equations is a challenging and computationally demanding problem. For this reason, often the application of a simpler statistical regression is preferred. In general, the regression models predict the biophysical parameter of interest from the corresponding received radiance, learning a mapping from in situ data. However, this approach does not employ the physical information encoded in the RTMs. An alternative strategy, which attempts to include the physical knowledge, consists in learning a regression model trained using simulated data by an RTM code. In this paper, we introduce a nonlinear nonparametric regression model that combines the benefits of the two aforementioned approaches. The inversion is performed considering jointly both real observations and RTMsimulated data. The proposed joint Gaussian process (JGP) provides a solid framework for exploiting the regularities between the two types of data, in order to perform inverse modeling. The JGP automatically detects the relative quality of the simulated and real data, and combines them properly. This occurs by learning an additional hyperparameter with respect to a standard Gaussian process model, so that the novel scheme is at the same time simple and robust, i.e., capable of adapting to different scenarios. The advantages of the JGP method compared with benchmark strategies are shown considering synthetic and real data in different experiments. Specifically, we consider leaf area index retrieval from Landsat data combined with simulated data generated by the PROSAIL model. [ABSTRACT FROM AUTHOR]

Current remote sensing image classification problems have to deal with an unprecedented amount of heterogeneous and complex data sources. Upcoming missions will soon provide large data streams that will make land cover/use classification difficult. Machine-learning classifiers can help at this, and many methods are currently available. A popular kernel classifier is the Gaussian process classifier (GPC), since it approaches the classification problem with a solid probabilistic treatment, thus yielding confidence intervals for the predictions as well as very competitive results to the state-of-theart neural networks and support vector machines. However, its computational cost is prohibitive for large-scale applications, and constitutes the main obstacle precluding wide adoption. This paper tackles this problem by introducing two novel efficient methodologies for GP classification. We first include the standard random Fourier features approximation into GPC, which largely decreases its computational cost and permits large-scale remote sensing image classification. In addition, we propose a model which avoids randomly sampling a number of Fourier frequencies and alternatively learns the optimal ones within a variational Bayes approach. The performance of the proposed methods is illustrated in complex problems of cloud detection from multispectral imagery and infrared sounding data. Excellent empirical results support the proposal in both computational cost and accuracy. [ABSTRACT FROM AUTHOR]

The infrared atmospheric sounding interferometer (IASI) is flying on board of the Metop satellite series, which is part of the EUMETSAT Polar System. Products obtained from IASI data represent a significant improvement in the accuracy and quality of the measurements used for meteorological models. Notably, the IASI collects rich spectral information to derive temperature and moisture profiles, among other relevant trace gases, essential for atmospheric forecasts and for the understanding of weather. Here, we investigate the impact of near-lossless and lossy compression on IASI L1C data when statistical retrieval algorithms are later applied. We search for those compression ratios that yield a positive impact on the accuracy of the statistical retrievals. The compression techniques help reduce certain amount of noise on the original data and, at the same time, incorporate spatial–spectral feature relations in an indirect way without increasing the computational complexity. We observed that compressing images, at relatively low bit rates, improves results in predicting temperature and dew point temperature, and we advocate that some amount of compression prior to model inversion is beneficial. This research can benefit the development of current and upcoming retrieval chains in infrared sounding and hyperspectral sensors. [ABSTRACT FROM PUBLISHER]

This paper introduces the use of single-layer and deep convolutional networks for remote sensing data analysis. Direct application to multi- and hyperspectral imagery of supervised (shallow or deep) convolutional networks is very challenging given the high input data dimensionality and the relatively small amount of available labeled data. Therefore, we propose the use of greedy layerwise unsupervised pretraining coupled with a highly efficient algorithm for unsupervised learning of sparse features. The algorithm is rooted on sparse representations and enforces both population and lifetime sparsity of the extracted features, simultaneously. We successfully illustrate the expressive power of the extracted representations in several scenarios: classification of aerial scenes, as well as land-use classification in very high resolution or land-cover classification from multi- and hyperspectral images. The proposed algorithm clearly outperforms standard principal component analysis (PCA) and its kernel counterpart (kPCA), as well as current state-of-the-art algorithms of aerial classification, while being extremely computationally efficient at learning representations of data. Results show that single-layer convolutional networks can extract powerful discriminative features only when the receptive field accounts for neighboring pixels and are preferred when the classification requires high resolution and detailed results. However, deep architectures significantly outperform single-layer variants, capturing increasing levels of abstraction and complexity throughout the feature hierarchy. [ABSTRACT FROM PUBLISHER]

We introduce a method for manifold alignment of different modalities (or domains) of remote sensing images. The problem is recurrent when a set of multitemporal, multisource, multisensor, and multiangular images is available. In these situations, images should ideally be spatially coregistered, corrected, and compensated for differences in the image domains. Such procedures require massive interaction of the user, involve tuning of many parameters and heuristics, and are usually applied separately. Changes of sensors and acquisition conditions translate into shifts, twists, warps, and foldings of the (typically nonlinear) manifolds where images lie. The proposed semisupervised manifold alignment (SS-MA) method aligns the images working directly on their manifolds and is thus not restricted to images of the same resolutions, either spectral or spatial. SS-MA pulls close together samples of the same class while pushing those of different classes apart. At the same time, it preserves the geometry of each manifold along the transformation. The method builds a linear invertible transformation to a latent space where all images are alike and reduces to solving a generalized eigenproblem of moderate size. We study the performance of SS-MA in toy examples and in real multiangular, multitemporal, and multisource image classification problems. The method performs well for strong deformations and leads to accurate classification for all domains. A MATLAB implementation of the proposed method is provided at http://isp. uv.es/code/ssma.htm. [ABSTRACT FROM PUBLISHER]