José M. B. Dias

Vertex component analysis: a fast algorithm to unmix hyperspectral data

Given a set of mixed spectral (multispectral or hyperspectral) vectors, linear spectral mixture analysis, or linear unmixing, aims at estimating the number of reference substances, also called endmembers, their spectral signatures, and their abundance fractions. This paper presents a new method for unsupervised endmember extraction from hyperspectral data, termed vertex component analysis (VCA). The algorithm exploits two facts: (1) the endmembers are the vertices of a simplex and (2) the affine transformation of a simplex is also a simplex. In a series of experiments using simulated and real data, the VCA algorithm competes with state-of-the-art methods, with a computational complexity between one and two orders of magnitude lower than the best available method.

Does independent component analysis play a role in unmixing hyperspectral data

Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2)sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.

Semisupervised Self-Learning for Hyperspectral Image Classification

Remotely sensed hyperspectral imaging allows for the detailed analysis of the surface of the Earth using advanced imaging instruments which can produce high-dimensional images with hundreds of spectral bands. Supervised hyperspectral image classification is a difficult task due to the unbalance between the high dimensionality of the data and the limited availability of labeled training samples in real analysis scenarios. While the collection of labeled samples is generally difficult, expensive, and time-consuming, unlabeled samples can be generated in a much easier way. This observation has fostered the idea of adopting semisupervised learning techniques in hyperspectral image classification. The main assumption of such techniques is that the new (unlabeled) training samples can be obtained from a (limited) set of available labeled samples without significant effort/cost. In this paper, we develop a new approach for semisupervised learning which adapts available active learning methods (in which a trained expert actively selects unlabeled samples) to a self-learning framework in which the machine learning algorithm itself selects the most useful and informative unlabeled samples for classification purposes. In this way, the labels of the selected pixels are estimated by the classifier itself, with the advantage that no extra cost is required for labeling the selected pixels using this machine-machine framework when compared with traditional machine-human active learning. The proposed approach is illustrated with two different classifiers: multinomial logistic regression and a probabilistic pixelwise support vector machine. Our experimental results with real hyperspectral images collected by the National Aeronautics and Space Administration Jet Propulsion Laboratorys Airborne Visible-Infrared Imaging Spectrometer and the Reflective Optics Spectrographic Imaging System indicate that the use of self-learning represents an effective and promising strategy in the context of hyperspectral image classification.

The Z/spl pi/M algorithm: a method for interferometric image reconstruction in SAR/SAS

This paper presents an effective algorithm for absolute phase (not simply modulo-2-pi) estimation from incomplete, noisy and modulo-2pi observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2-pi-periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss-Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step (Z-step), implemented by network programming techniques and an iterative conditional modes (ICM) step (pi-step). Accordingly, the algorithm is termed ZpiM, where the letter M stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2pi-multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is low-pass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach.

Nonparametric estimation of mean Doppler and spectral width

This paper proposes a new nonparametric method for estimation of spectral moments of a zero-mean Gaussian process immersed in additive white Gaussian noise. Although the technique is valid for any order moment, particular attention is given to the mean Doppler (first moment) and to the spectral width (square root of the centered second spectral moment). By assuming that the power spectral density (PSD) of the underlying process is bandlimited, the maximum-likelihood estimates of its spectral moments are derived. A suboptimal estimate based on the sample covariance is also studied. Both methods are robust in the sense that they do not rely on any assumption concerning the PSD (besides being bandlimited). Under weak conditions, the set of estimates based on sample covariance is unbiased and strongly consistent. Compared with the classical pulse pair and the periodogram-based estimators, the proposed methods exhibit better statistical properties for asymmetric spectra and/or spectra with large spectral widths, while involving a computational burden of the same order.

Fast GEM wavelet-based image deconvolution algorithm

The paper proposes a new wavelet-based Bayesian approach to image deconvolution, under the space-invariant blur and additive white Gaussian noise assumptions. Image deconvolution exploits the well known sparsity of the wavelet coefficients, described by heavy-tailed priors. The present approach admits any prior given by a linear (finite of infinite) combination of Gaussian densities. To compute the maximum a posteriori (MAP) estimate, we propose a generalized expectation maximization (GEM) algorithm where the missing variables are the Gaussian modes. The maximization step of the EM algorithm is approximated by a stationary second order iterative method. The result is a GEM algorithm of O(N log N) computational complexity. In comparison with state-of-the-art methods, the proposed algorithm either outperforms or equals them, with low computational complexity.The paper proposes a new wavelet-based Bayesian approach to image deconvolution, under the space-invariant blur and additive white Gaussian noise assumptions. Image deconvolution exploits the well known sparsity of the wavelet coefficients, described by heavy-tailed priors. The present approach admits any prior given by a linear (finite of infinite) combination of Gaussian densities. To compute the maximum a posteriori (MAP) estimate, we propose a generalized expectation maximization (GEM) algorithm where the missing variables are the Gaussian modes. The maximization step of the EM algorithm is approximated by a stationary second order iterative method. The result is a GEM algorithm of O(N log N) computational complexity. In comparison with state-of-the-art methods, the proposed algorithm either outperforms or equals them, with low computational complexity.

A new technique for hyperspectral compressive sensing using spectral unmixing

In Hyperspectral imaging the sensors measure the light refelcted by the earth surface in differents wavelenghts, usually the number of measures is between one and several hundreds per pixel. This generates huge data ammounts that must be transmitted to the earth and for subsequent processing. The real-time requirements of some applications make that the bandwidth required between the sensor and the earth station is very large. The Compressive Sensing (CS) framework tries to solve this problem. Althougth the hyperspectral images have thousands of bands usually most of the bands are highly correlated. The CS exploit this feature of the hyperspectral images and allow to represent most of the information in few bands instead of hundreds. This compressed version of the data can be sent to a earth station that will recover the original image using the corresponding algorithm. In this paper we describe an Compressive Sensing algorithm called Hyperspectral Coded Aperture (HYCA) that was developed in previous works. This algorithm has a parameter that need to be optimized empirically in order to get the better results. In this work we present a novel way to reconstruct the compressed images under the HYCA framework in which we do not need to optimize any parameter due to all parameters can be estimated automatically. The results show that this new way to reconstruct the images without the parameter provides similar results with respect to the best parameter setting for the old algorithm. The proposed approach have been tested using synthetic data and also we have used the dataset obtained by the AVIRIS sensor of NJPL over the Cuprite mining district in Nevada.

Adaptive restoration of speckled SAR images using a compound random Markov field

This paper proposes a restoration scheme for noisy images generated by coherent imaging systems (e.g., synthetic aperture radar, synthetic aperture sonar ultrasound imaging, and laser imaging). The approach is Bayesian: the observed image intensity is assumed to be a random variable with gamma density; the image to be restored (mean amplitude) is modeled by a compound Gauss-Markov random field which enforces smoothness on homogeneous regions while preserving discontinuities between neighboring regions. A Neyman-Pearson detection criterion is used to infer the discontinuities, thus allowing to select a given false alarm probability maximizing the detection probability. The whole restoration scheme is then cast into a maximum a posteriori probability (MAP) problem. An expectation maximization type iterative scheme embedded in a continuation algorithm is used to compute the MAP solution. An application example performed on radar data is presented.

Adaptive Bayesian Contour Estimation: A Vector Space Representation Approach

We propose a vector representation approach to contour estimation from noisy data. Images are modeled as random fields composed of a set of homogeneous regions; contours (boundaries of homogeneous regions) are assumed to be vectors of a subspace of L2(T) generated by a given finite basis; B-splines, Sinc-type, and Fourier bases are considered. The main contribution of the paper is a smoothing criterion, interpretable as a priori contour probability, based on the Kullback distance between neighboring densities. The maximum a posteriori probability (MAP) estimation criterion is adopted. To solve the optimization problem one is led to (joint estimation of contours, subspace dimension, and model parameters), we propose a gradient projection type algorithm. A set of experiments performed on simulated an real images illustrates the potencial of the proposed methodology

Does Independent Component Analysis Play a~Role in Unmixing Hyperspectral Data?

Independent component analysis (ICA) has recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: 1) the observed spectrum vector is a linear mixture of the constituent spectra (endmember spectra) weighted by the correspondent abundance fractions (sources); 2)sources are statistically independent. Independent factor analysis (IFA) extends ICA to linear mixtures of independent sources immersed in noise. Concerning hyperspectral data, the first assumption is valid whenever the multiple scattering among the distinct constituent substances (endmembers) is negligible, and the surface is partitioned according to the fractional abundances. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be statistically independent, this compromising the performance of ICA/IFA algorithms in hyperspectral unmixing. This paper studies the impact of hyperspectral source statistical dependence on ICA and IFA performances. We conclude that the accuracy of these methods tends to improve with the increase of the signature variability, of the number of endmembers, and of the signal-to-noise ratio. In any case, there are always endmembers incorrectly unmixed. We arrive to this conclusion by minimizing the mutual information of simulated and real hyperspectral mixtures. The computation of mutual information is based on fitting mixtures of Gaussians to the observed data. A method to sort ICA and IFA estimates in terms of the likelihood of being correctly unmixed is proposed.