Abstract-Kernel-based algorithms have been a topic of considerable interest in the machine learning community over the last ten years. Their attractiveness resides in their elegant treatment of nonlinear problems. They have been successfully applied to pattern recognition, regression and density estimation. A common characteristic of kernel-based methods is that they deal with kernel expansions whose number of terms equals the number of input data, making them unsuitable for online applications. Recently, several solutions have been proposed to circumvent this computational burden in time series prediction problems. Nevertheless, most of them require excessively elaborate and costly operations. In this paper, we investigate a new model reduction criterion that makes computationally demanding sparsification procedures unnecessary. The increase in the number of variables is controlled by the coherence parameter, a fundamental quantity that characterizes the behavior of dictionaries in sparse approximation problems. We incorporate the coherence criterion into a new kernel-based affine projection algorithm for time series prediction. We also derive the kernel-based normalized LMS algorithm as a particular case. Finally, experiments are conducted to compare our approach to existing methods.

When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM).However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multi-scattering effects or intimate interactions. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM.In this paper, we present an overview of recent advances in nonlinear unmixing modeling.arXiv:1304.1875v2 [physics.data-an]

This paper studies the statistical behavior of an affine combination of the outputs of two least mean-square (LMS) adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor ( ) is restricted to the interval (0,1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the mean-square error (MSE). First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSDs of either filter.

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can greatly benefit from spatial regularization strategies. However, existing spatial regularization strategies lead to large-scale nonsmooth optimization problems. Thus, efficiently introducing spatial context in the unmixing problem remains a challenge, and a necessity for many real world applications. In this paper, a novel multiscale spatial regularization approach for sparse unmixing is proposed. The method uses a signal-adaptive spatial multiscale decomposition based on segmentation and over-segmentation algorithms to decompose the unmixing problem into two simpler problems, one in an approximation image domain and another in the original domain. Simulation results using both synthetic and real data indicate that the proposed method outperforms stateof-the-art Total Variation-based algorithms with a computation time comparable to that of their unregularized counterparts.

Endmember variability is an important factor for accurately unveiling vital information relating the pure materials and their distribution in hyperspectral images. Recently, the extended linear mixing model (ELMM) has been proposed as a modification of the linear mixing model (LMM) to consider endmember variability effects resulting mainly from illumination changes. In this paper, we further generalize the ELMM leading to a new model (GLMM) to account for more complex spectral distortions where different wavelength intervals can be affected unevenly. We also extend the existing methodology to jointly estimate the variability and the abundances for the GLMM. Simulations with real and synthetic data show that the unmixing process can benefit from the extra flexibility introduced by the GLMM.Index Terms-Hyperspectral data, GLMM, endmember variability.

Image fusion combines data from different heterogeneous sources to obtain more precise information about an underlying scene. Hyperspectral-multispectral (HS-MS) image fusion is currently attracting great interest in remote sensing since it allows the generation of high spatial resolution HS images, circumventing the main limitation of this imaging modality. Existing HS-MS fusion algorithms, however, neglect the spectral variability often existing between images acquired at different time instants. This time difference causes variations in spectral signatures of the underlying constituent materials due to different acquisition and seasonal conditions. This paper introduces a novel HS-MS image fusion strategy that combines an unmixingbased formulation with an explicit parametric model for typical spectral variability between the two images. Simulations with synthetic and real data show that the proposed strategy leads to a significant performance improvement under spectral variability and state-of-the-art performance otherwise.

The spectral signatures of the materials contained in hyperspectral images (HI), also called endmembers (EM), can be significantly affected by variations in atmospheric, illumination or environmental conditions typically occurring within an HI. Traditional spectral unmixing (SU) algorithms neglect the spectral variability of the endmembers, what propagates significant mismodeling errors throughout the whole unmixing process and compromises the quality of its results. Therefore, large efforts have been recently dedicated to mitigate the effects of spectral variability in SU. This resulted in the development of algorithms that incorporate different strategies to allow the EMs to vary within an HI, using, for instance, sets of spectral signatures known a priori, Bayesian, parametric, or local EM models. Each of these approaches has different characteristics and underlying motivations. This paper presents a comprehensive literature review contextualizing both classic and recent approaches to solve this problem. We give a detailed evaluation of the sources of spectral variability and their effect in HI spectra. Furthermore, we propose a new taxonomy that organizes existing work according to a practitioner's point of view, based on the necessary amount of supervision and on the computational cost they require. We also review methods used to construct spectral libraries (which are required by many SU techniques) based on the observed HI, as well as algorithms for library augmentation and reduction. Finally, we conclude the paper with some discussions and an outline of possible future directions for the field.

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