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This paper analyzes the classification of hyperspectral remote sensing images with linear discriminant analysis (LDA) in the presence of a small ratio between the number of training samples and the number of spectral features. In these particular ill-posed problems, a reliable LDA requires one to introduce regularization for problem solving. Nonetheless, in such a challenging scenario, the resulting regularized LDA (RLDA) is highly sensitive to the tuning of the regularization parameter. In this context, we introduce in the remote sensing community an efficient version of the RLDA recently presented by Ye et al. to cope with critical ill-posed problems. In addition, several LDA-based classifiers (i.e., penalized LDA, orthogonal LDA, and uncorrelated LDA) are compared theoretically and experimentally with the standard LDA and the RLDA. Method differences are highlighted through toy examples and are exhaustively tested on several ill-posed problems related to the classification of hyperspectral remote sensing images. Experimental results confirm the effectiveness of the presented RLDA technique and point out the main properties of other analyzed LDA techniques in critical ill-posed hyperspectral image classification problems. Index Terms--Hyperspectral images, ill-posed problem, image classification, linear discriminant analysis (LDA), regularization.

Hyperspectral remote sensing images are affected by different types of noise. In addition to typical random noise, nonperiodic partially deterministic disturbance patterns generally appear in the data. These patterns, which are intrinsic to the image formation process, are characterized by a high degree of spatial and spectral coherence. We present a new technique that faces the problem of removing the spatially coherent noise known as vertical striping, usually found in images acquired by push-broom sensors. The developed methodology is tested on data acquired by the Compact High Resolution Imaging Spectrometer (CHRIS) onboard the Project for On-board Autonomy (PROBA) orbital platform, which is a typical example of a push-broom instrument exhibiting a relatively high noise component. The proposed correction method is based on the hypothesis that the vertical disturbance presents higher spatial frequencies than the surface radiance. A technique to exclude the contribution of the spatial high frequencies of the surface from the destriping process is introduced. First, the performance of the proposed algorithm is tested on a set of realistic synthetic images with added modeled noise in order to quantify the noise reduction and the noise estimation accuracy. Then, algorithm robustness is tested on more than 350 real CHRIS images from different sites, several acquisition modes (different spatial and spectral resolutions), and covering the full range of possible sensor temperatures. The proposed algorithm is benchmarked against the CHRIS reference algorithm. Results show excellent rejection of the noise pattern with respect to the original CHRIS images, especially improving the removal in those scenes with a natural high contrast. However, some low-frequency components still remain. In addition, the developed correction model captures and corrects the dependency of the noise patterns on sensor temperature, which confirms the robustness of the presented approach. OCIS codes: 030.1670, 030.4280, 100.3020, 110.4234, 280.4788.

This paper studies the performance and applicability of a novel kernel partial least squares (KPLS) algorithm for nonlinear feature extraction in the context of remote sensing applications. The so-called kernel orthonormalized PLS algorithm with reduced complexity (rKOPLS) has the following two core parts: 1) a kernel version of OPLS (called KOPLS) and 2) a sparse approximation for large-scale data sets, which ultimately leads to the rKOPLS algorithm. The method is theoretically analyzed in terms of computational burden and memory requirements and is tested in common remote sensing applications: multi- and hyperspectral image classification and biophysical parameter estimation problems. The proposed method largely outperforms the traditional (linear) PLS algorithm and demonstrates good capabilities in terms of expressive power of the extracted nonlinear features, accuracy, and scalability as compared to the standard KPLS. Index Terms--Feature extraction, image classification, kernel methods, model inversion, partial least squares (PLS), support vector machine (SVM).

This paper presents a methodology for cloud screening of multispectral images acquired with the Medium Resolution Imaging Spectrometer (MERIS) instrument on-board the Environmental Satellite (ENVISAT). The method yields both a discrete cloud mask and a cloud-abundance product from MERIS level-1b data on a per-pixel basis. The cloud-screening method relies on the extraction of meaningful physical features (e.g., brightness and whiteness), which are combined with atmospheric-absorption features at specific MERIS-band locations (oxygen and watervapor absorptions) to increase the cloud-detection accuracy. All these features are inputs to an unsupervised classification algorithm; the cloud-probability output is then combined with a spectral uumixing procedure to provide a cloud-abundance product instead of binary flags. The method is conceived to be robust and applicable to a broad range of actual situations with high variability of cloud types, presence of ground covers with bright and white spectra, and changing illumination conditions or observation geometry. The presented method has been shown to outperform the MERIS level-2 cloud flag in critical cloud-screening situations, such as over ice/snow covers and around cloud borders. The proposed modular methodology constitutes a general framework that can be applied to multispectral images acquired by spaceborne sensors working in the visible and near-infrared spectral range with proper spectral information to characterize atmospheric-oxygen and water-vapor absorptions. Index Terms--Cloud screening, Medium Resolution Imaging Spectrometer (MERIS), multispectral images, spectral unmixing, unsupervised classification.

A new approach based on the support vector machines (SVM) signal processing framework is presented for interpolation of nonuniformly sampled signals. Findings reveal that the SVM approach provides a robust but indirect estimation of the coefficients and is also closer in its nature to YenSs optimal formulation.

This paper addresses the problem of supervised classification of remote sensing images in the presence of incomplete (nonexhaustive) training sets. The problem is analyzed according to two different perspectives: 1) description and recognition of a specific land-cover class by using single-class classifiers and 2) solution of multiclass problems with single-class classification techniques. In this framework, we analyze different one-class classifiers and introduce in the remote sensing community the support vector domain description method (SVDD). The SVDD is a kernel-based method that exhibits intrinsic regularization ability and robustness versus low numbers of high-dimensional samples. The SVDD technique is compared with other standard single-class methods both in problems focused on the recognition of a single specific land-cover class and in multiclass problems. For the latter, we properly define an easily scalable multiclass architecture capable to deal with incomplete training data. Experimental results, obtained on different kinds of data (synthetic, hyperspectral, and multisensor images), point out the effectiveness of the SVDD technique and provide important indications for driving the choice of the classification technique and architecture in the presence of incomplete training data. Index Terms--Image classification, incomplete training data, kernel methods, one-class domain description, remote sensing, support vector domain description (SVDD).

We introduce two support vector machine (SVM)-based approaches for solving antenna problems such as beamforming, sidelobe suppression, and maximization of the signal-to-noise ratio. A basic introduction to SVM optimization is provided and a complex nonlinear SVM formulation developed to handle antenna array processing in space and time. The new optimization formulation is compared with both the minimum mean square error and the minimum variance distortionless response methods. Several examples are included to show the performance of the new approaches. Index Terms--Antenna arrays, beamforming, kernel method, Mercer's kernels, support vector machines.

Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARM[A.sub.2K]) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based system identification nonlinear models is presented, based on the use of composite Mercer's kernels. This general class can improve model flexibility by emphasizing the input-output cross information (SVM-ARM[A.sub.4K]), which leads to straightforward and natural combinations of implicit and explicit ARMA models (SVR-ARM[A.sub.2K] and SVR-ARM[A.sub.4K]). Capabilities of these different SVM-based system identification schemes are illustrated with two benchmark problems.

Support vector machine (SVM) learning has been recently proposed for image compression in the frequency domain using a constant s-insensitivity zone by Robinson and Kecman [1]. However, according to the statistical properties of natural images and the properties of human perception, a constant insensitivity makes sense in the spatial domain but it is certainly not a good option in a frequency domain. In fact, in their approach, they made a fixed low-pass assumption as the number of discrete cosine transform (DCT) coefficients to be used in the training was limited. This paper extends the work of Robinson and Kecman by proposing the use of adaptive insensitivity SVMs [2] for image coding using an appropriate distortion criterion [3], [4] based on a simple visual cortex model. Training the SVM by using an accurate perception model avoids any a priori assumption and improves the rate-distortion performance of the original approach. Index Terms--Adaptive insensitivity, discrete cosine transform (DCT), image coding, maximum perceptual error, perceptual metric, support vector machine (SVM).

This paper presents the framework of kernel-based methods in the context of hyperspectral image classification, illustrating from a general viewpoint the main characteristics of different kernel-based approaches and analyzing their properties in the hyperspectral domain. In particular, we assess performance of regularized radial basis function neural networks (Reg-RBFNN), standard support vector machines (SVMs), kernel Fisher discriminant (KFD) analysis, and regularized AdaBoost (Reg-AB). The novelty of this work consists in: 1) introducing Reg-RBFNN and Reg-AB for hyperspectral image classification; 2) comparing kernel-based methods by taking into account the peculiarities of hyperspectral images; and 3) clarifying their theoretical relationships. To these purposes, we focus on the accuracy of methods when working in noisy environments, high input dimension, and limited training sets. In addition, some other important issues are discussed, such as the sparsity of the solutions, the computational burden, and the capability of the methods to provide outputs that can be directly interpreted as probabilities. Index Terms--AdaBoost, feature space, hyperspectral classification, kernel-based methods, kernel Fisher discriminant analysis, radial basis function neural networks, regularization, support vector machines.

A novel fuzzy-based activation function for artificial neural networks is proposed. This approach provides easy hardware implementation and straightforward interpretability in the basis of IF-THEN rules. Backpropagation learning with the new activation function also has low computational complexity. Several application examples (XOR gate, chaotic time-series prediction, channel equalization, and independent component analysis) support the potential of the proposed scheme. Index Terms--Activation function, fuzzy logic, rule extraction.

The external administration of recombinant human erythropoietin is the chosen treatment for those patients with secondary anemia due to chronic renal failure in periodic hemodialysis. The objective of this paper is to carry out an individualized prediction of the EPO dosage to be administered to those patients. The high cost of this medication, its side-effects and the phenomenon of potential resistance which some individuals suffer all justify the need for a model which is capable of optimizing dosage individualization. A group of 110 patients and several patient factors were used to develop the models. The support vector regressor (SVR) is benchmarked with the classical multilayer perceptron (MLP) and the Autoregressive Conditional Heteroskedasticity (ARCH) model. We introduce a priori knowledge by relaxing or tightening the [epsilon]-insensitive region and the penalization parameter depending on the time period of the patients' follow-up. The so-called profile-dependent SVR (PD-SVR) improves results of the standard SVR method and the MLP. We perform sensitivity analysis on the MLP and inspect the distribution of the support vectors in the input and feature spaces in order to gain knowledge about the problem. Index Terms--Anemia, chronic renal failure, clinical pharmacokinetics, drug monitoring, erythropoietin, neural networks, support vector method, time series prediction.

This paper proposes the use of neural networks for individualizing the dosage of cyclosporine A (CyA) in patients who have undergone kidney transplantation. Since the dosing of CyA usually requires intensive therapeutic drug monitoring, the accurate prediction of CyA blood concentrations would decrease the monitoring frequency and, thus, improve clinical outcomes. Thirty-two patients and different factors were studied to obtain the models. Three kinds of networks (multilayer perceptron, finite impulse response (FIR) network, and Elman recurrent network) and the formation of neural-network ensembles are used in a scheme of two chained models where the blood concentration predicted by the first model constitutes an input to the dosage prediction model. This approach is designed to aid in the process of clinical decision making. The FIR network, yielding root-mean-square errors (RMSEs) of 52.80 ng/mL and mean errors (MEs) of 0.18 ng/mL in validation (10 patients) showed the best blood concentration predictions and a committee of trained networks improved the results (RMSE = 46.97 ng/mL, ME = 0.091 ng/mL). The Elman network was the selected model for dosage prediction (RMSE = 0.27 mg/Kg/d, ME = 0.07 mg/Kg/d). However, in both cases, no statistical differences on the accuracy of neural methods were found. The models' robustness is also analyzed by evaluating their performance when noise is introduced at input nodes, and it results in a helpful test for models' selection. We conclude that neural networks can be used to predict both dose and blood concentrations of cyclosporine in steady-state. This novel approach has produced accurate and validated models to be used as decision-aid tools. Index Terms--Blood concentration, clinical pharmacokinetics, cyclosporine, drug monitoring, kidney transplantation, neural networks, time series prediction.