Although multimodal remote sensing data analysis can strongly improve the characterization of physical phenomena on Earth's surface, nonidealities and estimation imperfections between records and investigation models can limit its actual information extraction ability. In this article, we aim at predicting the maximum information extraction that can be reached when analyzing a given data set. By means of an asymptotic information theory-based approach, we investigate the reliability and accuracy that can be achieved under optimal conditions for multimodal analysis as a function of data statistics and parameters that characterize the multimodal scenario to be addressed. Our approach leads to the definition of two indices that can be easily computed before the actual processing takes place. Moreover, we report in this article how they can be used for operational use in terms of image selection in order to maximize the robustness of the multimodal analysis, as well as to properly design data collection campaigns for understanding and quantifying physical phenomena. Experimental results show the consistency of our approach.

In this paper, we are interested in optimal sensor placement for signal extraction. Recently, a new criterion based on output signal to noise ratio has been proposed for sensor placement. However, to solve the optimization problem, a greedy approach is used over a grid, which is not optimal. To improve this method, we present an optimization approach to locate all the sensors at once. We further add a constraint to the problem that controls the average distances between the sensors. To solve our problem, we use an alternating optimization penalty method. As the associated cost function is non-convex, the proposed algorithm should be carefully initialized. We propose to initialize it with the result of the greedy method. Experimental results show the superiority of the proposed method over the greedy approach.

This work aims to propose an approach for pruning a bagging ensemble regression (BER) model based on sparse representation, which we call sparse representation pruning (SRP). Firstly, a BER model with a specific number of subensembles should be trained. Then, the BER model is pruned by our sparse representation idea. For this type of regression problems, pruning means to remove the subensembles that do not have a significant effect on prediction of the output. The pruning problem is casted as a sparse representation problem, which will be solved by orthogonal matching pursuit (OMP) algorithm. Experiments show that the pruned BER with only 20% of the initial subensembles has a better generalization compared to a complete BER.

In dictionary learning, a desirable property for the dictionary is to be of low mutual and average coherences. Mutual coherence is defined as the maximum absolute correlation between distinct atoms of the dictionary, whereas the average coherence is a measure of the average correlations. In this paper, we consider a dictionary learning problem regularized with the average coherence and constrained by an upper-bound on the mutual coherence of the dictionary. Our main contribution is then to propose an algorithm for solving the resulting problem based on convexly approximating the cost function over the dictionary. Experimental results demonstrate that the proposed approach has higher convergence rate and lower representation error (with a fixed sparsity parameter) than other methods, while yielding similar mutual and average coherence values.

In literature, we find many examples showing that, contrary to what one might think, multimodal remote sensing analysis might be suboptimal. Given the high computational complexity typically required by multimodal investigation in order to properly extract information from multiple sources, there is a need to assess its actual benefit during image preprocessing. This urgency becomes indeed crucial when targeting transfer learning in remote sensing, as understanding the actual relationship between diverse sensors is fundamental to accurately characterize the considered scenes. In this work, we derive a reliability metric by means of an information theory-based approach. The proposed metric is able to estimate how confident one can be of the considered datasets when characterizing each pixel in the considered region of interest. Experimental results on real datasets show how this quantity can be used to improve the understanding of the scenes, and to enhance multisensor transfer learning.

In hyperspectral imaging, spectral unmixing aims at decomposing the image into a set of reference spectral signatures corresponding to the materials present in the observed scene and their relative proportions in every pixel. While a linear mixing model was used for a long time, the complex nature of the physicochemical phenomena that affect the spectra of the materials led to shift the community's attention toward algorithms accounting for the variability of the endmembers. Such intraclass variations are mainly due to local changes in the composition of the materials and to illumination changes. In the physical remote sensing community, a popular model accounting for illumination variability is the radiative transfer model proposed by Hapke. It is, however, too complex to be directly used in hyperspectral unmixing in a tractable way. Instead, the extended linear mixing model (ELMM) allows to easily unmix the hyperspectral data accounting for changing illumination conditions and to address nonlinear effects to some extent. In this letter, we show that the ELMM can be obtained from the Hapke model by successively simplifying physical assumptions, whose validity we experimentally examine, thus demonstrating its relevance to handle illumination-induced variability in the unmixing problem.

A brain-computer interface (BCI) is a common device for communication between the human brain and a computer. This article investigates the efficiency of using a 3-D interface for BCI machines. For this purpose, the P300 speller, which is a BCI device that enables the user to spell characters on a screen using brain waves, is modified. The classical virtual keyboard of the P300 speller is replaced with 3-D stereoscopic images, which enhances the ergonomic features of the device. Moreover, the flashing paradigm on a 3-D interface can affect the performance of the device in three ways: accuracy, speed, and capacity. This article proposes two different flashing paradigms called the natural 3-D and parallel 2-D interfaces and studied their effects regarding the three mentioned measures. The former flashes the planes in 3-D space, and the latter comprises flashes of parallel keyboards at different 3-D depths. The theoretical analysis of these effects is presented. The results are validated by experimental data obtained from real subjects and were compared with the classical 2-D interface. Both presented keyboards increase the speed of the device, while parallel 2-D has a better total performance than natural 3-D.

Hyperspectral image unmixing has proven to be a useful technique to interpret hyperspectral data, and is a prolific research topic in the community. Most of the approaches used to perform linear unmixing are based on convex geometry concepts, because of the strong geometrical structure of the linear mixing model. However, many algorithms based on convex geometry are still used in spite of the underlying model not considering the intra-class variability of the materials. A natural question is to wonder to what extent these concepts and tools (Intrinsic Dimensionality estimation, endmember extraction algorithms, pixel purity) are still relevant when spectral variability comes into play. In this paper, we first analyze their robustness in a case where the linear mixing model holds in each pixel, but the endmembers vary in each pixel according to a prescribed variability model. In the light of this analysis, we propose an integrated unmixing chain which tries to adress the shortcomings of the classical tools used in the linear case, based on our previously proposed extended linear mixing model. We show the interest of the proposed approach on simulated and real datasets.

This paper focuses on the optimal sensor placement problem with the purpose of signal extraction in an underdetermined noisy setting. Assuming prior information on the spatial gain of the measured signal and on the spatial noise correlation, we propose a sensor placement criterion based on the maximization of the average signal to noise ratio of the estimated signal. Our approach differs from classical Kriging based optimal sensor placement approaches, since the latter focus on best reconstruction of the spatial measured field and not on the estimation of an underlying signal. Performance analysis of the proposed criterion is presented along with synthetic results. It is observed that sensor placement with our criterion significantly outperforms other methods based on Kriging.

Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the observations are usually mixtures of the contributions of several materials. The spectral unmixing problem aims at recovering the spectra of the pure materials of the scene (endmembers), along with their proportions (abundances) in each pixel. In order to deal with the intra-class variability of the materials and the induced spectral variability of the endmembers, several spectra per material, constituting endmember bundles, can be considered. However, the usual abundance estimation techniques do not take advantage of the particular structure of these bundles, organized into groups of spectra. In this paper, we propose to use group sparsity by introducing mixed norms in the abundance estimation optimization problem. In particular, we propose a new penalty, which simultaneously enforces group and within-group sparsity, to the cost of being nonconvex. All the proposed penalties are compatible with the abundance sum-to-one constraint, which is not the case with traditional sparse regression. We show on simulated and real datasets that well-chosen penalties can significantly improve the unmixing performance compared to classical sparse regression techniques or to the naive bundle approach.

This paper deals with the identifiability of joint independent subspace analysis of real-valued Gaussian stationary data with uncorrelated samples. This model is not identifiable when each mixture is considered individually. Algebraically, this model amounts to coupled block decomposition of several matrices. In previous work, we showed that if all the cross-correlations in this model were square matrices, the model was generally identifiable. In this paper, we show that this does not necessarily hold when the cross-correlation matrices are rectangular. In this current contribution, we first show that, in certain cases, the balance of degrees of freedom (d.o.f.) between model and observations does not allow identifiability; this situation never occurs in the square case. Second, we explain why for certain block sizes, even if the balance of d.o.f. seems adequate, the model is never identifiable.

Local Spectral Unmixing (LSU) methods perform the unmixing of hyperspectral data locally in regions of the image. The endmembers and their abundances in each pixel are extracted region-wise, instead of globally to mitigate spectral variability effects, which are less severe locally. However, it requires the local estimation of the number of endmembers to use. Algorithms for intrinsic dimensionality (ID) estimation tend to overestimate the local ID, especially in small regions. The ID only provides an upper bound of the application and scale dependent number of endmembers, which leads to extract irrelevant signatures as local endmembers, associated with meaningless local abundances. We propose a method to select in each region the best subset of the locally extracted endmembers. Collaborative sparsity is used to detect spurious endmembers in each region and only keep the most influent ones. We compute an algorithmic regularization path for this problem, giving access to the sequence of successive active sets of endmembers when the regularization parameter is increased. Finally, we select the optimal set in the sense of the Bayesian Information Criterion (BIC), favoring models with a high likelihood, while penalizing those with too many endmembers. Results on real data show the interest of the proposed approach.

In this paper, a proof is provided to show that Gaussian signals will lose their Gaussianity if they are passed through a polynomial of an order greater than 1. This can help in blind compensation of polynomial nonlinearities on Gaussian sources by forcing the output to follow a Gaussian distribution (the term “blind” refers to lack of any prior information about the nonlinear function). It may have many applications in different fields of nonlinear signal processing for removing the nonlinearity. Particularly, in nonlinear blind source separation, it can be used as a pre-processing step to transform the problem to a linear one, which is already well studied in the literature. This idea is proposed, proved, and finally verified by a simple simulation as a proof of concept in this paper.

In this letter, we investigated the connection between information and estimation measures for mismatched Gaussian models. In addition to the input prior mismatch, we take into account the noise mismatch and establish a new relation between relative entropy and excess mean square error. The derived formula shows that the input prior mismatch may be canceled by the noise mismatch. Finally, an example illustrates the impact of model mismatches on estimation accuracy.

Hyperspectral image unmixing is a source separation problem whose goal is to identify the signatures of the materials present in the imaged scene (called endmembers), and to estimate their proportions (called abundances) in each pixel. Usually, the contributions of each material are assumed to be perfectly represented by a single spectral signature and to add up in a linear way. However, the main two limitations of this model have been identified as nonlinear mixing phenomena and spectral variability, i.e., the intraclass variability of the materials. The former limitation has been addressed by designing nonlinear mixture models, whereas the second can be dealt with by using (usually linear) space varying models. The typical example is a linear mixing model where the sources can vary from one pixel to the other. In this letter, we show that a recent variability model can also estimate the abundances of nonlinear mixtures to some extent. We make the theoretical connection between nonlinear models and this variability model, and confirm it with experiments on nonlinearly generated synthetic datasets.

A difficult aspect of multimodal estimation is the possible discrepancy between the sampling rates and/or the noise levels of the considered data. Many algorithms cope with these dissimilarities empirically. In this paper, we propose a conceptual analysis of multimodality where we try to find the "optimal" way of combining modalities. More specifically, we consider a simple Kalman filtering framework where several noisy sensors with different sampling frequences and noise variances regularly observe a hidden state. We experimentally underline some relationships between the sampling grids and the asymptotic variance of the maximum a posteriori (MAP) estimator. However, the explicit study of the asymptotic variance seems intractable even in the simplest cases. We describe a promising idea to circumvent this difficulty: exploiting a stochastic measurement model for which one can more easily study the average asymptotic behavior.

In this paper, we present an alternative proof for characterizing the (non-) identifiability conditions of independent vector analysis (IVA). IVA extends blind source separation to several mixtures by taking into account statistical dependencies between mixtures. We focus on IVA in the presence of real Gaussian data with temporally independent and identically distributed samples. This model is always non-identifiable when each mixture is considered separately. However, it can be shown to be generically identifiable within the IVA framework. Our proof differs from previous ones by being based on direct factorization of a closed-form expression for the Fisher information matrix. Our analysis is based on a rigorous linear algebraic formulation, and leads to a new type of factorization of a structured matrix. Therefore, the proposed approach is of potential interest for a broader range of problems.

We apply social ℓ-norms for the first time to the problem of hyperspectral unmixing while modeling spectral variability. These norms are built with inter-group penalties which are combined in a global intra-group penalization that can enforce selection of entire endmember bundles; this results in the selection of a few representative materials even in the presence of large endmembers bundles capturing each material's variability. We demonstrate improvements quantitatively on synthetic data and qualitatively on real data for three cases of social norms: group, elitist, and a fractional social norm, respectively. We find that the greatest improvements arise from using either the group or fractional flavor.

The intrinsic dimensionality (ID) of multivariate data is a very important concept in spectral unmixing of hyperspectral images. A good estimation of the ID is crucial for a correct retrieval of the number of endmembers (the spectral signatures of macroscopic materials) in the image, for dimensionality reduction or for subspace learning, among others. Recently, some approaches to perform spectral unmixing and superresolution locally have been proposed, which require a local estimation of the number of endmembers to use. However, the role of ID in local regions of hyperspectral images has not been properly addressed. Some important issues when dealing with small regions of hyperspectral data can seriously affect the performance of conventional hyperspectral ID estimators. We show that three factors mainly affect local ID estimation: the number of pixels in the local regions, which has to be high enough for the estimations to be relevant, the number of hyperspectral bands which complicates the estimations if the ambient space has a high dimensionality, and the noise, which can be misinterpreted as a signal when its power is important. Here, we review the hyperspectral ID estimators on the literature for local ID estimation, we show how they behave in a local setting on synthetic and real data sets, and we provide some guidelines to make proper use of these estimators in local approaches.

In this paper, we consider the problem of unmixing a time series of hyperspectral images. We propose a dynamical model based on linear mixing processes at each time instant. The spectral signatures and fractional abundances of the pure materials in the scene are seen as latent variables, and assumed to follow a general dynamical structure. Based on a simplified version of this model, we derive an efficient spectral unmixing algorithm to estimate the latent variables by performing alternating minimizations. The performance of the proposed approach is demonstrated on synthetic and real multitemporal hyperspectral images.

In the above-named work, the support information in the first footnote is corrected.

A common approach to blind source separation is to use independent component analysis. However when dealing with realistic convolutive audio and speech mixtures, processing in the frequency domain at each frequency bin is required. As a result this introduces the permutation problem, inherent in independent component analysis, across the frequency bins. Independent vector analysis directly addresses this issue by modeling the dependencies between frequency bins, namely making use of a source prior. An alternative source prior for real-time (online) natural gradient independent vector analysis is proposed. A Student's t probability density function is known to be more suited for speech sources, due to its heavier tails, and is incorporated into a real-time version of natural gradient independent vector analysis. In addition, the importance of the degrees of freedom parameter within the Student's t distribution is highlighted. The final algorithm is realized as a real-time embedded application on a floating point Texas Instruments digital signal processor platform, where simulated recordings from a reverberant room are used for testing. Results are shown to be better than with the original (super-Gaussian) source prior.

In this paper we address the problem of image interpolation using Gaussian Mixture Models (GMM) as a prior. Previous methods of image restoration with GMM have not considered spatial (geometric) distance between patches in clustering, failing to fully exploit the coherency of nearby patches. The GMM framework in our method for image interpolation is based on the assumption that the accumulation of similar patches in a neighborhood are derived from a multivariate Gaussian probability distribution with a specific covariance and mean. An Expectation Maximization-like (EM-like) algorithm is used in order to determine patches in a cluster and restore them. The results show that our image interpolation method outperforms previous state-of-the-art methods with an acceptable bound.

The articles in this special issue focus on multimodal data fusion. These papers provide a review of current approaches and results on multimodal data fusion from different disciplines, and by including the required background in each domain, aims to provide a common forum for the exchange of ideas in this very active field of research.

In various disciplines, information about the same phenomenon can be acquired from different types of detectors, at different conditions, in multiple experiments or subjects, among others. We use the term “modality” for each such acquisition framework. Due to the rich characteristics of natural phenomena, it is rare that a single modality provides complete knowledge of the phenomenon of interest. The increasing availability of several modalities reporting on the same system introduces new degrees of freedom, which raise questions beyond those related to exploiting each modality separately. As we argue, many of these questions, or “challenges,” are common to multiple domains. This paper deals with two key issues: “why we need data fusion” and “how we perform it.” The first issue is motivated by numerous examples in science and technology, followed by a mathematical framework that showcases some of the benefits that data fusion provides. In order to address the second issue, “diversity” is introduced as a key concept, and a number of data-driven solutions based on matrix and tensor decompositions are discussed, emphasizing how they account for diversity across the data sets. The aim of this paper is to provide the reader, regardless of his or her community of origin, with a taste of the vastness of the field, the prospects, and the opportunities that it holds.

This paper, investigates the use of a 3D setting for Brain-Computer Interface (BCI) by implementing the 3D interface for the P300-Speller device. The 3D configurations were implemented using two different approaches which are called Natural 3D and Parallel 2D. The theoretical analyses concerning these two approaches are provided considering the modifications in speed, accuracy, and capacity. The experimental results on subjects who tested the 3D interfaces are then provided to validate the theoretical analyses.

The automatic detection of Electrocardiogram (ECG) waves is important to cardiac disease diagnosis. A good performance of an automatic ECG analyzing system depends heavily upon the accurate and reliable detection of QRS complex, as well as P and T waves. In this paper, we propose an efficient method for extraction of characteristic points of ECG signal. The method is based on a nonlinear dynamic model, previously introduced for generation of synthetic ECG signals. For estimating the parameters of model, we use an Extendend Kalman Filter (EKF). By introducing a simple AR model for each of the dynamic parameters of Gaussian functions in model and considering separate states for ECG waves, the new EKF structure was constructed. Quantitative and qualitative evaluations of the proposed method have been done on Physionet QT database (QTDB). This method is also compared with another EKF approach (EKF17). Results show that the proposed method can detect fiducial points of ECG precisely and mean and standard deviation of estimation error do not exceed two samples (8 msec).

This tutorial paper aims at summarizing some problems, ranging from analytical chemistry to novel chemical sensors, that can be addressed with classical or advanced methods of signal and image processing. We gather them under the denomination of “chemical sensing”. It is meant to introduce the special session “Signal Processing for Chemical Sensing” with a large overview of issues which have been and remain to be addressed in this application domain, including chemical analysis leading to PARAFAC/tensor methods, hyper spectral imaging, ion-sensitive sensors, artificial nose, chromatography, mass spectrometry, etc. For enlarging and illustrating the points of view of this tutorial, the invited papers of the session consider other applications (NMR, Raman spectroscopy, recognition of explosive compounds, etc.) addressed by various methods, e.g. source separation, Bayesian, and exploiting typical chemical signal priors like positivity, linearity, unit-concentration or sparsity.

During the last decade, there has been a growing interest toward the problem of sparse decomposition. A very important task in this field is dictionary learning, which is designing a suitable dictionary that can sparsely represent a group of training signals. In most dictionary learning algorithms, the cost function to determine the the optimum dictionary is the ℓ0norm of the matrix of decomposition coefficients of the training signals. However, we believe that this cost function fails to fully express the goal of dictionary learning, because it only sparsifies the whole set of coefficients for all training signals, rather than the coefficients for each training signal individually. Thus, in this paper we present a new criterion for dictionary learning. We then propose a new dictionary learning algorithm that solves our proposed optimization problem for the case of complete dictionaries. The proposed algorithm follows the idea of smoothed ℓ0(SL0) algorithm for sparse recovery. Simulation results emphasize the efficiency of the proposed cost function and algorithm.

A dictionary learning problem is a matrix factorization in which the goal is to factorize a training data matrix, Y, as the product of a dictionary, D, and a sparse coefficient matrix, X, as follows, Y ≃ DX. Current dictionary learning algorithms minimize the representation error subject to a constraint on D (usually having unit column-norms) and sparseness of X. The resulting problem is not convex with respect to the pair (D,X). In this letter, we derive a first order series expansion formula for the factorization, DX. The resulting objective function is jointly convex with respect to D and X. We simply solve the resulting problem using alternating minimization and apply some of the previously suggested algorithms onto our new problem. Simulation results on recovery of a known dictionary and dictionary learning for natural image patches show that our new problem considerably improves performance with a little additional computational load.

We consider a geometrical approach for solving the Nonnegative Blind Source Separation (N-BSS) problem in the case of noiseless linear instantaneous mixture model. When the sources are nonnegative, the scatter plot of the mixed data is contained in the simplicial cone generated by the mixing matrix. The proposed method, called Simplicial Cone Shrinking Algorithm for Unmixing Nonnegative Sources (SCSA-UNS), estimates the mixing matrix and the sources by finding the Minimum Volume (MV) simplicial cone containing all the mixed data. Simulations on synthetic data shows the efficiency of the proposed method.

In this paper, we address the matrix completion problem and propose a novel algorithm based on a smoothed rank function (SRF) approximation. Among available algorithms like FPCA and OptSpace, there is no solution that can simultaneously cover wide range of easy and hard problems. This new algorithm provides accurate results in almost all scenarios with a reasonable run time. It especially has low execution time in hard problems where other methods need long time to converge. Furthermore, when the rank is known in advance and is high, our method is very faster than previous methods for the same accuracy. The main idea of the algorithm is based on a continuous and differentiable approximation of the rank function and then, using gradient projection approach to minimize it.

Independent Component Analysis (ICA) is a well-known technique for solving blind source separation (BSS) problem. However “classical” ICA algorithms seem not suited for non-negative sources. This paper proposes a gradient descent approach for solving the Non-Negative Independent Component Analysis problem (NNICA). NNICA original separation criterion contains the discontinuous sign function whose minimization may lead to ill convergence (local minima) especially for sparse sources. Replacing the discontinuous function by a continuous one tanh, we propose a more accurate regularized Gradient algorithm called “Exact” Regularized Gradient (ERG) for NNICA. Experiments on synthetic data with different sparsity degrees illustrate the efficiency of the proposed method and a comparison shows that the proposed ERG outperforms existing methods.

This paper presents a novel method for the enhancement of spatial quality of Hyperspectral (HS) images while making use of a high resolution panchromatic (PAN) image. Due to the high number of bands the application of a pansharpening technique to HS images may result in an increase of the computational load and complexity. Thus a dimensionality reduction preprocess, compressing the original number of measurements into a lower dimensional space, becomes mandatory. To solve this problem we propose a pansharpening technique combining both dimensionality reduction and fusion, exploited by non-linear Principal Component Analysis (NLPCA) and Indusion respectively, to enhance the spatial resolution of a hyperspectral image.

The unsupervised classification of hyperspectral images containing mixed pixels is addressed in this paper. Hyperspectral images are characterized by a trade-off between the spectral and the spatial resolution, this leading to data sets containing mixed pixels, e.g. pixels jointly occupied by more than a single land cover class. In [1], a preliminary research based on spectral unmixing concepts was conducted, in order to handle mixed pixels and to obtain thematic maps at a finer spatial resolution. In this work, we extend the investigation by proposing a new methodology based on image clustering. Experiments conducted on real data show the comparative effectiveness of the proposed method, which provides good results in terms of accuracy and is less sensitive to pixels with extreme values of reflectance.

In this paper, the use of Independent Component (IC) Discriminant Analysis (ICDA) for remote sensing classification is proposed. ICDA is a nonparametric method for discriminant analysis based on the application of a Bayesian classification rule on a signal composed by ICs. The method uses IC Analysis (ICA) to choose a transform matrix so that the transformed components are as independent as possible. When the data are projected in an independent space, the estimates of their multivariate density function can be computed in a much easier way as the product of univariate densities. A nonparametric kernel density estimator is used to compute the density functions of each IC. Finally, the Bayes rule is applied for the classification assignment. In this paper, we investigate the possibility of using ICDA for the classification of hyperspectral images. We study the influence of the algorithm used to enforce independence and of the number of IC retained for the classification, proposing an effective method to estimate the most suitable number. The proposed method is applied to several hyperspectral images, in order to test different data set conditions (urban/agricultural area, size of the training set, and type of sensor). Obtained results are compared with one of the most commonly used classifier of hyperspectral images (support vector machines) and show the comparative effectiveness of the proposed method in terms of accuracy.

Let${\bf A}$be an$n \times m$matrix with$m > n$, and suppose that the underdetermined linear system${\bf A} {\bf s} = {\bf x}$admits a sparse solution${\bf s}_0$for which$\Vert {\bf s}_0\Vert_0 < {1\over 2} {\rm spark}({\bf A})$. Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now that we have somehow a solution$\mathhat{\bf s}$as an estimation of${\bf s}_0$, and suppose that$\mathhat{\bf s}$is only “approximately sparse,” that is, many of its components are very small and nearly zero, but not mathematically equal to zero. Is such a solution necessarily close to the true sparsest solution? More generally, is it possible to construct an upper bound on the estimation error$\Vert \mathhat{\bf s}-{\bf s}_0\Vert_2$without knowing${\bf s}_0$? The answer is positive, and in this paper, we construct such a bound based on minimal singular values of submatrices of${\bf A}$. We will also state a tight bound, which is more complicated, but besides being tight, enables us to study the case of random dictionaries and obtain probabilistic upper bounds. We will also study the noisy case, that is, where${\bf x} = {\bf A} {\bf s}+{\bf n}$. Moreover, we will see that where$\Vert{{\bf s}_0}\Vert_0$grows, to obtain a predetermined guaranty on the maximum of$\Vert{\mathhat{\bf s}-{\bf s}_0}\Vert_2,$$\mathhat{\bf s}$is needed to be sparse with a better approximation. This can be seen as an explanation to the fact that the estimation quality of sparse recovery algorithms degrades where$\Vert{{\bf s}_0}\Vert_0$grows.

Independent Component Analysis (ICA) can be used to decompose functional Magnetic Resonance Imaging (fMRI) data into a set of statistically independent images which are likely to be the sources of fMRI data. After applying ICA, a set of independent components are produced, and then, a “meaningful” subset from these components must be identified, because a large majority of components are non-interesting. So, interpreting the components is an important and also difficult task. In this paper, we propose a criterion based on the entropy of time courses to automatically select the components of interest. This method does not require to know the stimulus pattern of the experiment.

In this paper, we suggest to use a steepest descent algorithm for learning a parametric dictionary in which the structure or atom functions are known in advance. The structure of the atoms allows us to find a steepest descent direction of parameters instead of the steepest descent direction of the dictionary itself. We also use a thresholded version of Smoothed-ℓ0(SL0) algorithm for sparse representation step in our proposed method. Our simulation results show that using atom structure similar to the Gabor functions and learning the parameters of these Gabor-like atoms yield better representations of our noisy speech signal than non parametric dictionary learning methods like K-SVD, in terms of mean square error of sparse representations.

International audience

This paper presents a link between the well known Common Spatial Pattern (CSP) algorithm and Riemannian geometry in the context of Brain Computer Interface (BCI). It will be shown that CSP spatial filtering and Log variance features extraction can be resumed as a computation of a Riemann distance in the space of covariances matrices. This fact yields to highlight several approximations with respect to the space topology. According to these conclusions, we propose an improvement of classical CSP method.

We propose a novel blind source separation method tailored for retrieving baseband signals having different bandwidths. Such a configuration is characterized by the existence of inactive bands in the frequency domain. By exploiting the eigenstructure of the mixtures covariance matrix calculated in these inactive bands, we develop a simple yet efficient extraction procedure that works in an ordered fashion, in which the sources are extracted according to their degree of smoothness. Numerical results attest the viability of the proposal.

In this brief, the optimally pruned extreme learning machine (OP-ELM) methodology is presented. It is based on the original extreme learning machine (ELM) algorithm with additional steps to make it more robust and generic. The whole methodology is presented in detail and then applied to several regression and classification problems. Results for both computational time and accuracy (mean square error) are compared to the original ELM and to three other widely used methodologies: multilayer perceptron (MLP), support vector machine (SVM), and Gaussian process (GP). As the experiments for both regression and classification illustrate, the proposed OP-ELM methodology performs several orders of magnitude faster than the other algorithms used in this brief, except the original ELM. Despite the simplicity and fast performance, the OP-ELM is still able to maintain an accuracy that is comparable to the performance of the SVM. A toolbox for the OP-ELM is publicly available online.

Sparse Decomposition (SD) of a signal on an overcomplete dictionary has recently attracted a lot of interest in signal processing and statistics, because of its potential application in many different areas including Compressive Sensing (CS). However, in the current literature, the dictionary matrix has generally been assumed to be of full-rank. In this paper, we consider non-full-rank dictionaries (which are not even necessarily overcomplete), and extend the definition of SD over these dictionaries. Moreover, we present an approach which enables to use previously developed SD algorithms for this non-full-rank case. Besides this general approach, for the special case of the Smoothed ℓ0(SL0) algorithm, we show that a slight modification of it covers automatically non-full-rank dictionaries.

In the last few years, we have witnessed an explosion in applications of sparse representation, the majority of which share the need for finding sparse solutions of underdetermined systems of linear equations (USLE's). Based on recently proposed smoothed lscr0-norm (SL0), we develop a noise-tolerant algorithm for sparse representation, namely Robust-SL0, enjoying the same computational advantages of SL0, while demonstrating remarkable robustness against noise. The proposed algorithm is developed by adopting the corresponding optimization problem for noisy settings, followed by theoretically-justified approximation to reduce the complexity. Stability properties of robust-SL0 are rigorously analyzed, both analytically and experimentally, revealing a remarkable improvement in performance over SL0 and other competing algorithms, in the presence of noise.

In this paper, we consider sparse decomposition (SD) of two-dimensional (2D) signals on overcomplete dictionaries with separable atoms. Although, this problem can be solved by converting it to the SD of one-dimensional (1D) signals, this approach requires a tremendous amount of memory and computational cost. Moreover, the uniqueness constraint obtained by this approach is too restricted. Then in the paper, we present an algorithm to be used directly for sparse decomposition of 2D signals on dictionaries with separable atoms. Moreover, we will state another uniqueness constraint for this class of decomposition. Our algorithm is obtained by modifying the Smoothed L0 (SL0) algorithm, and hence we call it two-dimensional SL0 (2D-SL0).

Recently, a lot of research has been done on compressed sensing, capturing compressible signals using random linear projections to a space of radically lower dimension than the ambient dimension of the signal. The main impetus of this is that the radically dimension-lowering linear projection step can be done totally in analog hardware, in some cases even in constant time, to avoid the bottleneck in sensing and quantization steps where a large number of samples need to be sensed and quantized in short order, mandating the use of a large number of fast expensive sensors and A/D converters. Reconstruction algorithms from these projections have been found that come within distortion levels comparable to the state of the art in lossy compression algorithms. This paper considers a variation on compressed sensing that makes it resistant to spiky noise. This is achieved by an analog real-field error-correction coding step. It results in a small asymptotic overhead in the number of samples, but makes exact reconstruction under spiky measurement noise, one type of which is the salt and pepper noise in imaging devices, possible. Simulations are performed that corroborate our claim and in fact substantially improve reconstruction under unreliable sensing characteristics and are stable even under small perturbations with Gaussian noise.

In this paper, we propose a Bayesian pursuit algorithm for sparse representation. It uses both the simplicity of the pursuit algorithms and optimal Bayesian framework to determine active atoms in sparse representation of a signal. We show that using Bayesian Hypothesis testing to determine the active atoms from the correlations leads to an efficient activity measure. Simulation results show that our suggested algorithm has better performance among the algorithms which have been implemented in our simulations in most of the cases.

Independent component analysis (ICA) is a very popular method that has shown success in blind source separation, feature extraction and unsupervised recognition. In recent years ICA has been largely studied by researchers from the signal processing community. This paper addresses a more in-depth study on the use of this method, applied to hyper-spectral images used for remote sensing purposes. In a first part, source separation is addressed. Since the independence of sources is usually not verified in hyperspectral real data images, ICA, if used alone, is not a suitable tool to unmix sources. We propose a hierarchical approximation for the use of ICA as a pre-processing step for a Bayesian Positive Source Separation method. In a second part, the use of ICA for dimensionality reduction is studied in the frame of hyperspectral data classification. Experimental results show the effectiveness of ICA when used for hyperspectral image pre-processing for the two considered applications.

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In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is presented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal itself) has a sparse representation on an overcomplete dictionary, and we are looking for the sparsest representation among the representations of all the shifted versions of s. Then, the proposed algorithm finds simultaneously the amount of the required shift, and the sparse representation. Experimental results emphasize on the performance of our algorithm.

In this paper we present an algorithm for complex-valued sparse representation. In our previous work we presented an algorithm for sparse representation based on smoothed lscrdeg- norm. Here we extend that algorithm to complex-valued signals. The proposed algorithm is compared to FOCUSS algorithm and it is experimentally shown that the proposed algorithm is about two or three orders of magnitude faster than FOCUSS while providing approximately the same accuracy.

In this paper, a new approach for decoding real-field codes based on finding sparse solutions of underdetermined linear systems is proposed. This algorithm iteratively estimates the positions and the amplitudes of the sparse errors (or noise impulses) using an expectation-maximization (EM) algorithm. Iterative estimation of amplitudes is done in the expectation step (E-step), while iterative estimation of error positions is done in the maximization step (M-step). Simulation results show 1-2 dB improvement over linear programming (LP) which has been previously used for error correction.

In this paper, new techniques to improve whisper-to-speech conversion are investigated, in the framework of silent speech telephone communication. A preliminary conversion method from Non-Audible Murmur (NAM) to modal speech, based on statistical mapping trained using aligned corpora has been proposed. Although it is a very promising technique, its performance is still insufficient due to the difficulties in estimating F0 from unvoiced speech. In this paper, two distinct modifications are proposed, in order to improve the naturalness of the synthesized speech. In the first modification, LDA (Linear Discriminant Analysis) is used instead of PCA (Principal Component Analysis) to reduce the dimensionality of the input spectral vectors. In addition, the influence of long-term variation of spectral information on pitch estimation is examined. The second modification is an attempt to integrate visual information as a complementary input to improve spectral estimation, F0 estimation and voicing decision.

In this letter, we address the theoretical limitations in estimating the mixing matrix in noisy sparse component analysis (SCA) for the two-sensor case. We obtain the Cramer-Rao lower bound (CRLB) error estimation of the mixing matrix. Using the Bernouli-Gaussian (BG) sparse distribution, and some simple assumptions, an approximation of the Fisher information matrix (FIM) is calculated. Moreover, this CRLB is compared to some of the main methods of mixing matrix estimation in the literature.

Abstract—This paper addresses the main goals and objec-tives of the Hyperspectral Imaging Network (HYPER-I-NET), a recently started Marie Curie Research Training Network. The project is designed to build an interdisciplinary research community focusing on hyperspectral imaging activities. The core strategy of the network is to create a powerful interdisciplinary synergy between different domains of expertise closely related to hyperspectral imaging activities in Europe, ranging from sensor design and flight operation to data collection, processing, interpretation, and dissemination. Our main goals in this paper are to present the project to the Geoscience and Remote Sensing community and to provide an overview of the planned activities in each sub-activity covered by the network.

Looking at the speaker's face can be useful to better hear a speech signal in noisy environment and extract it from competing sources before identification. This suggests that the visual signals of speech (movements of visible articulators) could be used in speech enhancement or extraction systems. In this paper, we present a novel algorithm plugging audiovisual coherence of speech signals, estimated by statistical tools, on audio blind source separation (BSS) techniques. This algorithm is applied to the difficult and realistic case of convolutive mixtures. The algorithm mainly works in the frequency (transform) domain, where the convolutive mixture becomes an additive mixture for each frequency channel. Frequency by frequency separation is made by an audio BSS algorithm. The audio and visual informations are modeled by a newly proposed statistical model. This model is then used to solve the standard source permutation and scale factor ambiguities encountered for each frequency after the audio blind separation stage. The proposed method is shown to be efficient in the case of 2 times 2 convolutive mixtures and offers promising perspectives for extracting a particular speech source of interest from complex mixtures

In this paper, we study the distribution of the log-modulus of a Gaussian complex random variable. In the circular case, it is a Log-Rayleigh (LR) variable, whose probability distribution function (pdf) depends on only one parameter. In the noncircular case, the pdf is more complicated, although we show that it can be adequately modeled by an LR pdf, for which the optimal fitting parameter is derived. These results can be used in any application using the log-modulus of discrete Fourier transform coefficients, e.g., for speech/audio signals, and suggest that a mixture of LR pdf kernels is preferable to more classical models such as mixtures of Gaussian kernels, which are more costly and less efficient

We present a new approach to the voice activity detection (VAD) problem for speech signals embedded in non-stationary noise. The method is based on automatic lipreading: the objective is to detect voice activity or non-activity by exploiting the coherence between the speech acoustic signal and the speaker's lip movements. From a comprehensive analysis of lip shape parameters during speech and non-speech events, we show that a single appropriate visual parameter, defined to characterize the lip movements, can be used for the detection of sections of voice activity or more precisely, for the detection of silence sections. Detection scores obtained on spontaneous speech confirm the efficiency of the visual voice activity detector (VVAD)

Looking at the speaker's face seems useful for hearing a speech signal better and extracting it from competing sources before identification. We present a novel algorithm plugging the audiovisual coherence of speech signals, estimated by statistical tools, on audio blind source separation (BSS) algorithms in the difficult case of convolutive mixtures. The algorithm mainly works in the frequency (transform) domain, where the convolutive mixture becomes an additive mixture for each frequency channel. Frequency by frequency separation is made by an audio BSS algorithm, and the audiovisual information is used to solve the standard source permutation and scale factor problems at the output of the separation stage, for each frequency. The proposed method is shown to be efficient in the case of 2/spl times/2 convolutive mixtures.

We derive a class of contrasts for blind source separation (BSS) to separate bounded sources (or more generally, finite sources), based on support width measures (SWM) of the marginal output distributions. These contrasts are shown to have no spurious local maxima, i.e., all the local maxima are relevant from the source separation point of view; they all correspond to non-mixing BSS solutions so that a gradient-ascent method can be used.

This letter deals with the resolution of the blind source separation problem using the independent component analysis method in post-nonlinear mixtures. Using the sole hypothesis of the source independence is not obvious to reconstruct the sources in nonlinear mixtures. Here, we prove the identifiability under weak assumptions on the mixture matrix and density sources.

A new algorithm for blind source separation in convolutive mixtures, based on minimizing the mutual information of the outputs, is proposed. This minimization is done using a recently proposed minimization-projection (MP) approach for minimizing mutual information in a parametric model. Since the minimization step of the MP approach is proved to have no local minimum, it is expected that this new algorithm has good convergence behaviour.

The work presents experimental comparison of two approaches introduced for solving the nonlinear blind source separation (BSS) problem: the Bayesian methods developed at Helsinki University of Technology (HUT), and the BSS methods introduced for post-nonlinear (PNL mixtures at Institut National Polytechnique de Grenoble (INPG). The comparison is performed on artificial test problems containing PNL mixtures. Both the standard case when the number of sources is equal to the number of observations and the case of overdetermined mixtures are considered. A new interesting result of the experiments is that globally invertible PNL mixtures, but with non-invertible component-wise nonlinearities, can be identified and sources can be separated, which shows the relevance of exploiting more observations than sources.

Looking at the speaker's face seems useful in hearing better a speech signal and extract it from the competing sources before identification. In this paper, we present a novel algorithm plugging audiovisual coherence of speech signals, estimated by statistical tools, on audio blind source separation (BSS) algorithms in the difficult case of convolutive mixtures. The algorithm mainly works in the frequency (transform) domain, where the convolutive mixture becomes an additive mixture for each frequency channel. Frequency by frequency separation is made by an audio BSS algorithm, and the audiovisual information is used to solve the standard source permutation problem at the output of the separation stage, for each frequency. The proposed method is shown to be efficient in the case of 2 /spl times/ 2 convolutive mixtures.

In this paper, we review recent advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixing models. After a general introduction to BSS and ICA, we discuss in more detail uniqueness and separability issues, presenting some new results. A fundamental difficulty in the nonlinear BSS problem and even more so in the nonlinear ICA problem is that they provide non-unique solutions without extra constraints, which are often implemented by using a suitable regularization. In this paper, we explore two possible approaches. The first one is based on structural constraints. Especially, post-nonlinear mixtures are an important special case, where a nonlinearity is applied to linear mixtures. For such mixtures, the ambiguities are essentially the same as for the linear ICA or BSS problems. The second approach uses Bayesian inference methods for estimating the best statistical parameters, under almost unconstrained models in which priors can be easily added. In the later part of this paper, various separation techniques proposed for post-nonlinear mixtures and general nonlinear mixtures are reviewed.

In this letter, we compute the variation of the mutual information, resulting from a small variation in its argument. Although the result can be applied in many problems, we consider only one example: the result is used for deriving a new method for blind source separation in linear mixtures. The experimental results emphasize the performance of the resulting algorithm.

It is well known that the source separation in a nonlinear case is, in general, impossible: there exist many mappings with nondiagonal Jacobian matrices preserving the independence. We suggest that using the time structure of the sources (if it exists), this indeterminacy may be reduced. In particular, we show that the classical examples used in the literature for demonstrating the nontrivial nonseparability of the nonlinear mixtures can be rejected by taking into account the temporal correlation of the sources.

This paper addresses the source separation in strong noisy mixtures by using wavelet de-noising processing. Experiments include the cases of white/correlated Gaussian and non-Gaussian noise, which correspond to various applications. The performance of BSS/ICA algorithms after wavelet de-noising is quantitatively investigated, and points out the efficiency of the method.

In many practical situations, the noise samples may be correlated. In this case, the estimation of noise parameters can be used to improve the approximation. Estimation of the noise structure can also be used to find a stopping criterion in constructive neural networks. To avoid overfitting, a network construction procedure must be stopped when residual can be considered as noise. The knowledge on the noise may be used for "whitening" the residual so that a correlation hypothesis test determines if the network growing must be continued or not. In this paper, supposing a Gaussian noise model, we study the problem of multi-output nonlinear regression using MLP when the noise in each output is a correlated autoregressive time series and is spatially correlated with other output noises. We show that the noise parameters can be determined simultaneously with the network weights and used to construct an estimator with a smaller variance, and so to improve the network generalization performance. Moreover, if a constructive procedure is used to build the network, the estimated parameters may be used to stop the procedure.

An underwater acoustic signals separation method based on prior information about the channel impulse response (IR) is presented. Using a sound speed profile measured in a real world environment, the IR of the ocean is estimated with normal mode theory and the ray tracing method. This propagation medium is characterized by a long duration finite IR composed alternatively of several intervals with null coefficients and peaks of non-zero amplitude that express the multi-path propagation. The channel IR characteristics are used as a prior knowledge to select intervals expected to contain non-zero coefficients to be adapted for separation filters estimation. Hence, the number of samples of filters to be adapted is highly reduced. The algorithm proposed by Yellin and Weinstein (1994) is used to successfully achieve the separation of two independent 16-QAM signals mixed in a realistic shallow water environment.

In this paper, supposing a Gaussian noise model, we study the problem of multi-output nonlinear regression using multilayer perceptrons (MLP) when the noise in each output is a correlated autoregressive time series and there is a spatial correlation between different output noise sources. We show that using a maximum likelihood approach, the noise parameters can be determined simultaneously with the network weights and used to improve the network generalization performance. For two special cases of first and second order AR noise, the appropriate cost functions to minimize them are derived.

This paper addresses the issue of hardware implementation of hierarchical neural principal component analysis (PCA). We attempt to show by experimental studies the effect of finite accuracy computations on the algorithm's performance, for both analog and digital implementation.

In this paper, we address the problem of the separation of convolutive mixtures in the case where the non-Gaussian source signals are not necessarily filtered versions of i.i.d. sequences. In this context, we show that the contrast functions, used in the linear process source case, still allow to separate the sources by a deflation approach. Some particular properties of higher order cumulants based contrast functions are also given.

This paper discusses some theoretical results on underdetermined source separation, i.e. when the mixing matrix is degenerate, especially when there is more sources than observations. In this case, we show that the sources can be restored up to an arbitrary additive random vector. In the particular case of discrete sources, very relevant for digital communications, we show that this vector is certain.

We propose an algorithm to model dynamic systems using constructive feedforward neural networks when the system output is corrupted with additive colored noise. The algorithm tries to whiten the approximation residue during the network construction. The whitened residue is also used to stop the algorithm and to avoid overfitting.

In this work, we point out some important properties of the normalized fourth-order cumulant (i.e., the kurtosis). In addition, we emphasize the relation between the signal distribution and the sign of the kurtosis. One should mention that in many situations, authors claim that the sign of the kurtosis depends on the nature of the signal (i.e., over- or sub-Gaussian). For a unimodal probability density function, that claim is true and is clearly proved in the letter. But for more complex distributions, it has been shown that the kurtosis sign may change with parameters and does not depend only on the asymptotic behavior of the distributions. Finally, these results give theoretical explanation to techniques, like nonpermanent adaptation, used in nonstationary situations.

This paper proposes a new approach for sources separation in special nonlinear mixtures, called post nonlinear mixtures (PNL). We first explain the nice separability properties of these mixtures: solutions have almost the same indeterminacies as in instantaneous linear mixtures. The method proposed in this paper is based on the minimization of the mutual information, which needs the knowledge of source distributions or more exactly of log-derivative of source distributions (the so-called score functions). The algorithm consists of three adaptive blocks: one nonlinear block is devoted to adaptive estimation of source score functions, and drives the adaptation of the two other blocks estimating the linear and nonlinear parts of the mixtures. The paper finishes with experimental results which illustrate the efficiency of the algorithm.