This article introduces a new method for decontaminating galaxy spectra within the framework of the Euclid space mission. Unlike our previously proposed methods that rely on a linear instantaneous model, this new method is based on a more realistic convolutive model. This model enables simultaneous decontamination and deconvolution of spectra, resulting in improved decontamination performance. First, we present a mixing model for observed data provided by four dispersion directions of light, transformed into the Fourier domain. Then, a method is proposed for estimating the spectrum of the object of interest. The effectiveness of the proposed method is demonstrated through preliminary results obtained using realistic noisy data.

In this paper, we propose an approach based on an Alternating Direction Method of Multipliers (ADMM) to unmix hyperspectral data using a recently proposed linear mixing model in which the spectral variability phenomenon is spectrally modeled in a multiplicative manner. This model allows for pixel-wise variation of the endmembers, resulting in different versions of the reference component spectra being considered in each pixel of the image. The proposed ADMM-based unmixing algorithm involves new iterative update rules. The investigation also evaluates the performance of the designed algorithm against some literature ones previously proposed. To this end, experiments using synthetic hyperspectral data are carried out. Overall, the obtained results prove that the proposed algorithm is very attractive for hyperspectral unmixing taking the spectral variability phenomenon into account.

Marine mucilage outbreaks not only pose a threat to the marine ecosystems, but also are a detriment to economy and public-health. The recent marine mucilage outbreak of Spring 2021 in the Sea of Marmara, Türkiye, was one of most serious recorded mucilage outbreaks, lasting over three months and covering more than 1000 square kilometers. Recently, linear spectral unmixing based environmental monitoring of marine mucilage from hyperspectral data have been shown to provide easy to interpret analysis of this complex phenomenon, in terms of endmember signatures and fractional abundances. This paper carries the work forward and proposes nonlinear unmixing for the environmental monitoring of marine mucilage. Hyperspectral data acquired by the PRISMA mission are used in this investigation.

Disasters in marine ecosystems, such as the outbreak of mucilage in the inland Sea of Marmara in the spring of 2021, raise serious environmental, economic and public health concerns. Recently, methods based on fully unsupervised unmixing and dealing with spectral variability have made it possible to analyze marine mucilage, quantify its abundance and thus to map this harmful phenomenon. This work proposes to use an informed (or semi-supervised) unmixing technique, which is based on nonnegative matrix factorization and dealing with spectral variability, using a field-measured spectrum of high-density (or accumulated) mucilage, in order to detect and map, in particular, this marine material. The used technique is evaluated on real hyperspectral PRISMA data, and compared with other unmixing-based techniques.

In these investigations, a new informed linear mixing model addressing spectral variability with an associated informed penalized hyperspectral unmixing algorithm is first proposed. This algorithm, which optimizes a new cost function with original iterative and multiplicative update rules, is based on nonnegative matrix factorization. Then, this algorithm is used for detecting and mapping several mineral deposits in the Algerian Central Hoggar. This method unmixes the considered PRISMA hyperspectral remote sensing data by exploiting known spectra of some minerals of interest. Obtained abundance fraction maps are then used to establish a classification map of the investigated area, with the considered mineral deposit classes, at a finer spatial resolution.

Hyperspectral data, acquired by air/spaceborne sensors, are generally exposed to intra-class variability, making their unmixing process more complicated, in terms of precise estimations of endmember spectra and their corresponding abundance fractions, by means of the usual linear mixing model that ignores this concern. Accordingly, further advanced linear mixing models, which address this issue, were proposed recently. Several of them consider this intra-class variability in the spectral part of variables, whereas many ones consider the same phenomenon in the spatial part of variables. In this investigation, a novel linear mixing model is proposed to deal with this phenomenon. This model considers this concern both in the spectral and spatial parts of variables. Moreover, an associated penalized hyperspectral unmixing algorithm, based on multiplicative nonnegative matrix factorization, is designed for the proposed model. This algorithm proves to be practical as obviously reported by conducted experiments and obtained results.

In this paper, we are interested in the blind separation of linear-quadratic mixtures of mutually independent sources when successive samples of each source are correlated. When a linear source separation method based on second-order statistics, like the well-known AMUSE method, is applied to this type of mixture, it provides subclasses of the initial mixture where each source can remain mixed with its square. We propose a new approach to then separate these two components. Simulations show the very good performance of our method, as compared with two other methods.

In this paper, a novel approach, based on a multistage informed spectral unmixing technique, for detecting and mapping several mineral deposits in the Gara-Djebilet region (Southwestern Algeria), is presented. The considered technique, which is related to linear spectral unmixing methods, uses an iterative informed multiplicative nonnegative matrix factorization algorithm. This technique unmixes the used PRISMA hyperspectral remote sensing data by exploiting known spectra of the considered minerals. More precisely, the originality of this work consists in applying iteratively, in two stages, the considered informed unmixing algorithm. During the first stage, abundant but irrelevant minerals, with known spectra and present in the considered region, are detected, and are then removed from the original hyperspectral data, which thus lead to the creation of new hyperspectral data to which the considered unmixing technique is applied, during the second stage, in order to detect and map other relevant minerals, with known spectra, and possibly together with unknown materials. Experiments are carried out with the considered real hyperspectral data, which cover the studied area, to assess the potential of the proposed approach. The obtained results are mainly confirmed and validated by prior knowledge of the investigated area.

Remote sensing hyperspectral images are usually subject to the intra-class variability phenomenon that complicates the precise estimation of endmember spectra and their abundance fractions when using the spectral unmixing process with the typical Linear Mixing Model (LMM), which ignores this concern. Thus, other refined LMMs, which deal with this issue, were developed. Some of them consider this spectral variability on the spectral part of variables, while other ones consider the same phenomenon on the spatial part of variables. In this work, a recent modified Augmented LMM (ALMM) is used to deal with the intra-class variability, considered on the spatial part of variables, by using smaller matrices that also obey the nonnegativity constraint. Furthermore, a projected gradient-based algorithm, based on Nonnegative Matrix Factorization (NMF), is proposed for the used modified ALMM. This Gradient-NMF-based technique proves to be useful as clearly reported by conducted experiments.

This paper presents a new Blind Source Separation (BSS) method for convolutive mixtures that can be underdeter-mined. Exploiting the sparsity of the source signals in the Time-Frequency (TF) domain, this method combines TF masking and beamforming. Indeed, on the one hand, BSS methods based on TF masking achieve remarkable performance even in the underdeter-mined case, however they tend to cause artifacts at the separated sources. On the other hand, beamforming can achieve good performance in the (over)-determined case without distorting the estimated signals. Therefore, combining these two techniques makes it possible to benefit from both their advantages. In the proposed method, unlike existing methods that use beamforming with TF masking, we introduce new normalized directional vectors to generate the different beamformers involved, and a new way for better estimating these vectors. In addition, we propose a new technique that can be used to separate sources in the case of underdetermined mixtures. Test results showed good performance for our method compared to various existing methods, similar in terms of working hypotheses, both in the determined and underdetermined cases.

Hypersharpening consists in generating an unobservable high-spatial-resolution hyperspectral image by fusing an observed low-spatial-resolution hyperspectral image with an observed high-spatial-resolution panchromatic or multispectral one. The obtained image preserves the high spectral resolution of the first image and the high spatial resolution of the second one. Unlike standard hypersharpening methods that do not consider the spectral variability phenomenon, in this letter, a new approach, which addresses this phenomenon, is proposed for fusing hyperspectral and multispectral remote sensing images. This approach, linked to linear spectral unmixing methods, is based on an extension of nonnegative matrix factorization (NMF), namely the inertia-constrained pixel-by-pixel NMF (IP-NMF) algorithm. The developed fusion algorithm, called hyperspectral and multispectral data fusion based on IP-NMF (HMF-IPNMF), is applied to synthetic and real data sets. Experimental results clearly show that the developed fusion method yields sharpened hyperspectral images with higher spectral and spatial fidelities when compared to those provided by tested state-of-the-art methods that do not take spectral variability into account.

In these investigations, an informed unmixing-based approach is considered for detecting and mapping several mineral deposits in the Algerian Central Hoggar. The considered technique, which is related to linear spectral unmixing methods, uses an informed multiplicative nonnegative matrix factorization algorithm. This technique unmixes the used hyperspectral remote sensing data by exploiting known spectra of the considered minerals. Experiments are carried out, to assess the potential of the used technique, on real hyperspectral PRecursore IperSpettrale della Missione Applicativa (PRISMA) data, which cover the considered study area. Obtained maps are analyzed by using a geological map of the investigated region.

Spectral unmixing methods aim at estimating a collection of pure material spectra and their associated proportions in each pixel of the image. Such methods usually suppose that each pure material is represented by a unique spectrum in all image pixels. However, in many cases this assumption is no more valid for materials that exhibit spectral variability due to varying illumination and atmospheric conditions or material composition. Recently, a novel linear mixing model that handles the spectral variability phenomenon, modeled in a multiplicative form, was proposed with an associated unmixing method. In the present paper, two gradient-based approaches, which use the above mixing model and that are based on pixel-by-pixel nonnegative matrix factorization, are proposed. The first approach uses the projected gradient descent algorithm, whereas the second one employs a Newton update. The proposed algorithms minimize a cost function that takes into account the considered linear mixing model with the spectral variability phenomenon. Experiments, based on realistic synthetic data, are conducted to evaluate the performance of the proposed algorithms. The obtained results are also compared to those of methods from the literature. These test results show that the proposed approaches prove to be very attractive for unmixing hyperspectral remote sensing data with spectral variability.

Remote sensing hyperspectral sensors are often limited in their spatial resolutions, which leads to mixed pixels. The linear spectral unmixing process is frequently used to extract endmember spectra and their abundance fractions. The standard linear mixing model considers that each endmember is represented by the same spectral signature in the entire image. However, such a basic hypothesis is not relevant in most practical situations since the spectral signature of an endmember can spatially vary. This intra-class variability phenomenon can be considered by introducing the concept of classes of endmembers. Recently, a structured additively-tuned linear mixing model, with its constraints, was proposed, with an associated unmixing method, to address this phenomenon. That method, based on Nonnegative Matrix Factorization (NMF), optimizes a cost function with iterative and multiplicative update rules supplemented by additional constraints that control the spectral variability. In the present work, two penalization terms that more efficiently manage the spectral variability are added to the considered cost function, for the same structured mixing model, and new NMF-based iterative and multiplicative update rules are deduced for achieving the unmixing process taking the considered phenomenon into account. The proposed algorithm proves to be very attractive as clearly reported by conducted experiments based on synthetic data.

Hyperspectral pansharpening methods, which aim to combine hyperspectral and panchromatic images, yield limited performance for scenes whose strong spatial heterogeneity induces mixed pixels. The SOSU method has been designed to handle this limitation and provided good results on agricultural and peri-urban landscapes. However, its performance was reduced on more complex urban scenes, which contain a higher proportion of mixed pixels. This article presents a new version of this method, called SOSU-2021, adapted to better process urban scenes. SOSU-2021 is tested on an urban dataset at a 1.6 m spatial resolution. We obtain better numerical results than with the previous SOSU version, and in the worst case, 56 % of the mixed pixels are better or equally processed by SOSU-2021 than by the method used as a reference.

In this work, a hypersharpening approach, creating fused hyperspectral remote sensing images with high spatial and spectral resolutions, is introduced. This approach, linked to linear spectral unmixing (LSU) methods and based on a multiplicative nonnegative matrix factorization (NMF) technique, extends the Joint-Criterion NMF (JCNMF) algorithm, by addressing the spectral variability phenomenon. This method is designed for combining low spatial resolution hyperspectral and high spatial resolution multispectral data. It optimizes the considered criterion that deals with the spectral variability phenomenon by using a specific structure of involved matrices. The introduced algorithm, which uses multiplicative and iterative update rules, is applied to realistic synthetic data, and its effectiveness, in the spatial and spectral domains, is evaluated by considering commonly used assessment protocol and performance criteria. The obtained results prove that the introduced algorithm yields fused hyperspectral data with good spectral and spatial fidelities. These results also illustrate that the proposed algorithm significantly outperforms two tested literature ones that do not take the spectral variability phenomenon into account.

We consider the problem of decontaminating galaxy spectra in the context of the EUCLID space mission. The spectra of neighboring astronomical objects being spatially mixed, a source separation method should be used to separate them. Here, we propose a new method based on the fusion of information between first and second-order spectra generated by a grism. Using the optical properties, we propose a regularized criterion and a gradient algorithm to optimize it. The tests using noisy realistic simulated data show that our method leads to better results than a method only based on second-order information.

In a very recent paper, we introduced (i) a specific hyper-spectral mixing model for the sea bottom, based on a detailed physical analysis which includes the adjacency effect, and (ii) an associated unmixing method, which is not blind in the sense that it requires a prior estimation of various parameters of that mixing model. We here proceed much further, by first analytically showing that this model can be seen as a specific member of the general class of mixing models involving spectral variability. Therefore, we then process such data with the IP-NMF and UP-NMF blind unmixing methods that we recently proposed in other works to handle spectral variability. Such a variability especially occurs when sea depth significantly varies over the considered scene, and we show that IP-NMF and UP-NMF then yield significantly better pure spectra estimation than a classical method from the literature which was not designed to handle such a variability.

Hyperspectral remote sensing data offer unique opportunities for the characterization of land surface in urban areas. However, no hyperspectral- unmixing based studies have been conducted to automatically detect photovoltaic panels, which represent one of the important components of energy systems in such areas. In this paper, a hyperspectral-unmixing based method is proposed to detect photovoltaic panels and to estimate their areas. This approach is based on an original multiplicative nonnegative matrix factorization (NMF) algorithm with some known photovoltaic panel spectra. The proposed method can be considered as a partial/informed NMF approach. Experiments are conducted on realistic synthetic and real data to evaluate the performance of the proposed approach. In both cases, obtained results show that the proposed method yields much better overall performance than a method from the literature.

A strong intern dynamic characterizes towns, a very high spatial heterogeneity of their elements, their 3D geometric shapes (horizontal and vertical) inducing shadows, and their large variety of materials. These characteristics make the collection of information of land surface properties and urban descriptors more delicate. Due to the enhancement of spatial to deepen the observation of urban areas. Nevertheless, such a type of sensors would not contribute to the characterization of the urban land surface properties (chemical composition of materials, species of vegetation, quality of soils, etc.). They and show great potentials might consider Hyperspectral imagery capacities as providing useful products but it becomes mandatory to define which type of information these different sensors can deliver. The ANR HYEP project has the purpose to demonstrate the benefit of a second generation of hyperspectral space borne mission characterized by a high spatial resolution (8m GSD) and a high temporal revisit. After a detailed description of the motivation of such a proposal, applications are given focused on urban vegetation, sealed and impervious areas, solar panel area estimation.

In this paper, a new approach is proposed for linear endmember spectra extraction from a highly mixed hyperspectral image combined with high spatial resolution multispectral data containing pure pixels. This new approach, which is applied to unmix the considered hyperspectral image, is based on a modified version of nonnegative matrix factorization (NMF) coupled with nonnegative least squares (NLS). The multispectral data are used to initialize the hyperspectral NMF algorithm and to constrain it during matrix updates. Experiments based on synthetic and real data are performed to evaluate the performance of the proposed approach and to compare it with five methods from the literature only applied to the hyperspectral data. The obtained performance shows the superiority of the proposed approach as compared with all other methods. Also, the impact, on the proposed method, of spectral variability between hyperspectral and multispectral data is evaluated, and the obtained results show the robustness of the proposed method to this variability.

Hypersharpening aims at combining an observable low-spatial resolution hyperspectral image with a high-spatial resolution remote sensing image, in particular a multispectral one, to generate an unobservable image with the high spectral resolution of the former and the high spatial resolution of the latter. In this paper, two such new fusion methods are proposed. These methods, related to linear spectral unmixing techniques, and based on nonnegative matrix factorization (NMF), optimize a new joint criterion and extend the recently proposed joint NMF (JNMF) method. The first approach, called gradient-based joint-criterion NMF (Grd-JCNMF), is a gradient-based method. The second one, called multiplicative JCNMF (Mult-JCNMF), uses new designed multiplicative update rules. These two JCNMF approaches are applied to synthetic and semireal data, and their effectiveness, in spatial and spectral domains, is evaluated with commonly used performance criteria. Experimental results show that the proposed JCNMF methods yield sharpened hyperspectral data with good spectral and spatial fidelities. The obtained results are compared with the performance of two NMF-based methods and one approach based on a sparse representation. These results show that the proposed methods significantly outperform the well-known coupled NMF sharpening method for most performance figures. Also, the proposed Mult-JCNMF method provides the results that are similar to those obtained by JNMF, with a lower computational cost. Compared with the tested sparse-representation-based approach, the proposed methods give better results. Moreover, the proposed Grd-JCNMF method considerably surpasses all other tested methods.

In this paper, we address the problem of spectral unmixing in urban hyperspectral images using a Maximum A Posteriori (MAP)-based Non-negative Matrix Factorization (NMF) approach. Considering a Linear-Quadratic (LQ) mixing model, we seek to decompose the spectrum observed in each pixel of the image into a set of pure material spectra, as well as their abundance fractions and the mixing coefficients associated with products of these pure material spectra. The main idea of the proposed method is to take into account the available prior information about the unknown parameters for a better estimation of them. To this end, we first derive a MAP-based cost function, then minimize it using a projected gradient algorithm by modifying a recently proposed NMF method adapted to LQ mixtures. Simulation results confirm the relevance of our approach.

In this paper, a new projected-gradient method for bilinear matrix factorization with nonnegativity constraints is proposed for extracting hyperspectral endmember spectra. The proposed method is designed for a bilinear mixing model faced in urban hyperspectral remote sensing images. Experiments based on realistic synthetic data, generated according to the considered bilinear mixing model, are conducted to evaluate the performance of the proposed method and of approaches from the literature. Experimental results show that the proposed method yields much better overall performance than the used literature approaches.

In this paper, we propose a new multi-sharpening approach for improving the spatial resolution of hyperspectral data. This approach, based on the linear-quadratic spectral unmixing concept, uses a linear-quadratic nonnegative matrix factorization multiplicative algorithm. Our method first consists in unmixing the low spatial resolution hyperspectral data and high spatial resolution multispectral data. The obtained high resolution spectral and spatial parts of information are then recombined, according to the linear-quadratic mixing model, in order to obtain unobservable multi-sharpened high spatial resolution hyperspectral data. Experiments, based on realistic synthetic and real data, are carried out to evaluate the performance of the proposed approach and of linear nonnegative matrix factorization-based approaches from the literature. We show that our proposed approach significantly outperforms the used literature methods.

Due to the limited spatial resolution of some remote sensing sensors, their image pixel spectra are commonly mixtures of elementary contributions. To analyze this type of images, it is necessary for some applications to perform spectral unmixing. This procedure allows the decomposition of a mixed pixel spectrum into a set of pure material spectra, and a set of abundance fractions. To this end, we here propose a new unsupervised spatial Blind Source Separation approach based on sparsity and geometrical properties. This approach first consists in finding small zones (composed of several adjacent pixels) containing only two sources using a spatial correlation-based method. This stage is followed by an identification stage where we geometrically estimate the pure material spectra. The final stage is the estimation of the searched abundances using a non-negative least squares method. The results obtained for simulated mixtures of realistic sources show the good performance of our method.

In the framework of Blind Quantum Source Separation, we investigate the adaptation of a separating system which receives coupled quantum bit (qubit) states and processes them with quantum means in its feedforward path, to uncouple them. We propose the first separation principle which ensures that the output qubit states of this system are disentangled and that they restore the non-entangled source qubit states up to limited indeterminacies. This separation principle exploits measurements of output spin components along two directions and has some links with the non-quantum Independent Component Analysis (ICA) principle. It opens the way to various practical separation criteria and algorithms, some of which are described here.

In the field of remote sensing, the unmixing of hyperspectral images is usually based on the use of a mixing model. Most existing spectral unmixing methods, used in the reflective range (0.4–2.5$\mu\hbox{m}$), rely on a linear model of endmember reflectances. Nevertheless, such a model supposes the pixels at the ground level to be uniformly irradiated and the scene to be flat. When considering a 3-D landscape, such a model is no longer valid as irradiated and shadowed areas are present, as well as radiative interactions between facing surfaces. This paper introduces a new mixing model adapted to urban environments and which aims to overcome these limitations. This model is derived from physical equations based on radiative transfer theory, and its analytic expression is linear–quadratic. Similar models have already been used in the literature for unmixing purposes but without being justified by physical analysis. Our proposed model is validated using a synthetic but realistic European 3-D urban scene. Then, simplifications are introduced, based on a study of the different radiative components contributing to the signal in a way to make the model easy to use for spectral unmixing. This paper also shows that the quadratic term cannot be neglected in many cases in urban environments since it can, e.g., range from 15% to 20% of the reflectances in canyons.

Remote sensing hyperspectral sensors typically collect data in contiguous narrow bands (up to several hundred bands) in the electromagnetic spectrum. In hyperspectral imagery, pixels are often linear mixtures of pure materials (endmembers) contained in the observed scene. In this paper, we propose a new unsupervised spatial method (called 2D-VM) for endmember spectra extraction from data to be collected by future higher spatial resolution hyperspectral sensors, which will allow the existence of some pure pixels. This method is related to the Blind Mixture Identification (BMI) problem, and is based on Sparse Component Analysis (SCA). It extracts the endmember spectra by using a spatial variance-based SCA method, which detects a few pure-pixel zones. Experiments based on synthetic but realistic data are performed to compare the performance of the proposed approach and of methods from the literature. We show that our approach outperforms all other methods.

In this paper, we propose Blind Source Separation (BSS) methods for possibly-correlated images, based on a low sparsity assumption. To satisfy this sparsity condition, one of the versions of our methods applies a wavelet transform to the observed images before performing separation. Another version directly operates in the original spatial domain, when the sources are sparse enough in this domain. Both methods consist in finding, in the considered sparse representation domain, tiny zones where only one source is active. The column of the mixing matrix corresponding to this source is then estimated in this zone. We also propose extensions of these methods, with automated selection of adequate analysis parameters. Various tests show the good performance of these approaches (SIR improvement often higher than 40 dB).

This letter presents a new maximum likelihood method for blindly separating linear instantaneous source mixtures, where source signals are assumed to be mutually independent, Markovian and possibly nonstationary. The proposed approach first extends previous works, by Hosseini to possibly nonstationary sources using two approaches based on blocking and kernel smoothing, respectively. Moreover, to reduce time consumption, we propose an equivariant modified Newton-Raphson algorithm to solve the estimating equations, and we introduce polynomial estimators for the conditional score functions used in our method. Experimental results, both for artificial and real (speech) signals, prove the better performance of our method as compared to various classical blind separation algorithms.

This paper presents a maximum likelihood approach for blindly separating linear instantaneous mixtures of images. The spatial autocorrelation within each image is described using nonsymmetrical half-plane (NSHP) Markov random fields in order to simplify the joint probability density functions of the source images. A first implementation assuming stationary sources is presented. It is then extended to a more realistic nonstationary image model: two approaches, respectively based on blocking and kernel smoothing, are proposed to cope with the nonstationarity of the images. The estimation of the mixing matrix is performed using an iterative equivariant version of the Newton-Raphson algorithm. Moreover, score functions, required for the computation of the updating rule, are approximated at each iteration by parametric polynomial estimators. Results achieved with artificial mixtures of both artificial and real-world images, including an astrophysical application, clearly prove the high performance of our methods, as compared to classical algorithms.

Blind source separation (BSS) and quantum information processing (QIP) are two recent and rapidly evolving fields. No connection has ever been made between them to our knowledge, except in our initial paper, However, future practical QIP systems will probably involve "observed mixtures", in the BSS sense, of quantum states (qubits), e.g. associated to coupled spins. We here investigate how individual qubits may be retrieved from cylindrical-symmetry Heisenberg-coupled versions of them, and we show the relationship between this problem and classical BSS. We thus introduce a new nonlinear mixture model for qubits, motivated by actual quantum physical devices. We analyze the invertibility and ambiguities of this model. We propose practical data processing methods for (i) estimating the mixing parameter with a maximum likelihood approach and (ii) performing inversion to retrieve the sources. This yields a major extension as compared to our previous paper, not only in terms of considered spin coupling model, but also because we here introduce a much more powerful mixture estimation procedure.

We propose an extension of EFICA algorithm for piecewise stationary and non Gaussian signals. The proposed method is able to profit from varying distribution of the original signals and also from their varying variance, which is demonstrated by simulations with real-world signals. We show that in case of constant-variance signals, the accuracy of the method may achieve the corresponding Cramer-Rao bound, if score functions of the original signals are known in all blocks.

We propose a time-frequency (TF) blind source separation (BSS) method suited to attenuated and delayed (AD) mixtures, inspired from a method that we previously developed for linear instantaneous mixtures. This approach only requires each of the uncorrelated sources to occur alone in a tiny TF zone, i.e. it sets very limited constraints on the source sparsity and overlap, unlike various previously reported TF-BSS methods. Our approach is based on time-frequency correlation (hence its name AD-TIFCORR). It consists in identifying the columns of the (filtered permuted) mixing matrix in TF zones where it detects that a single source occurs. We thus identify columns of scale coefficients and time shifts. This method is especially suited to non-stationary sources

This letter presents new blind separation methods for moving average (MA) convolutive mixtures of independent MA processes. They consist of time-domain extensions of the FastICA algorithms developed by Hyvarinen and Oja for instantaneous mixtures. They perform a convolutive sphering in order to use parameter-free fast fixed-point algorithms associated with kurtotic or negentropic non-Gaussianity criteria for estimating the source innovation processes. We prove the relevance of this approach by mapping the mixtures into linear instantaneous ones. Test results are presented for artificial colored signals and speech signals.

Most reported blind source separation (BSS) methods are based on independent component analysis (ICA), which esp. requires the sources to be stationary (and non-Gaussian). Time-frequency (TF) BSS methods avoid these restrictions and are therefore e.g. attractive for speech signals. We first introduce extensions of three types of TF-BSS methods that we recently proposed, and we analyze the relationships between these methods. We then provide a detailed benchmarking of these methods, based on a large number of tests performed with linear instantaneous mixtures of speech signals. This demonstrates the good performance of these methods (SNR typically above 60 dB) and their low sensitivity to the values of their TF parameters.

This paper concerns the underdetermined case of the convolutive source separation problem, i.e. the situation when the number of observed convolutively mixed signals is lower than the number of sources. We propose a criterion and associated algorithm which, unlike classical approaches, make it possible to perform the separation of a subset of these sources by exploiting their assumed non-stationarity properties. This approach uses the second-order statistics of the signals and adapts the filters of a direct separating system so as to cancel the "differential cross-correlation" of signals derived by this system. This new method is related to the general differential source separation concept that we proposed. Its effectiveness is shown by means of numerical tests.

This paper deals with the separation of two convolutively mixed signals. The proposed approach uses a recurrent structure adapted by a generic rule involving arbitrary separating functions. These functions should ideally be set so as to minimize the asymptotic error variance of the structure. However, these optimal functions are often unknown in practice. The proposed alternative is based on a self-adaptive (sub-)optimization of the separating functions, performed by estimating the projection of the optimal functions on a predefined set of elementary functions. The equilibrium and stability conditions of this rule and its asymptotic error variance are studied. Simulations are performed for real mixtures of speech signals. They show that the proposed approach yields much better performance than classical rules.

In this paper, we investigate the self-adaptive source separation problem for convolutively mixed signals. The proposed approach uses a recurrent structure adapted by a generic rule involving arbitrary separating functions. We first analyze the stability of this class of algorithms. We then apply these results to some classical rules for instantaneous and convolutive mixtures that were proposed in the literature but only partly analyzed. This provides a better understanding of the conditions of operation of these rules. Eventually, we define and analyze a normalized version of the proposed type of algorithms, which yields several attractive features.

The instruction set of digital integer-valued VLSIs implementing neural networks is typically restricted to weighted sums, threshold activation functions and weight assignments. However, neural networks also need divisions (for data normalizations) and root extractions (for distance or vector norm computations). This paper presents neural networks which perform the latter operations by using only the above basic instructions. These networks thus provide "macros" to the overall network which calls them. This yields a homogeneous environment. Moreover, a "virtual base" is introduced to exploit the available parallelism. It is freely chosen so as to achieve the desired trade-off between the speed and complexity of the proposed networks (with a minimum of only two neurons). This high-speed capability also makes these structures attractive independently from neural applications.