Saïd Moussaoui

The EUV Sun as the superposition of elementary Suns

Aims. Many studies assume that the solar irradiance in the EUV can be decomposed into different contributions, which makes modelling the spectral variability considerably easier. We consider a different approach in which these contributions are not imposed a priori but effectively and robustly inferred from spectral irradiance measurements. Methods. This is a source separation problem with a positivity constraint, for which we use a Bayesian solution. Results. Using five years of daily EUV spectra recorded by the TIMED/SEE satellite, we show that the spectral irradiance can be decomposed into three elementary spectra. Our results suggest that they describe different layers of the solar atmosphere rather than specific regions. The temporal variability of these spectra is discussed.

Source Separation in Chemical Analysis : Recent achievements and perspectives

Since its origins in the mid-1980s, the field of blind source separation (BSS) has attracted considerable attention within the signal processing community. One of the main reasons for such popularity is the existence of many problems that can be addressed in a BSS framework. Two noteworthy examples of applications can be found in audio and biomedical signal processing, for which a number of efficient solutions are now available. There are relevant BSS problems in other domains but on which less effort has been put. In this article, we deal with one of these fields, specifically the field of analytical chemistry (AC), whose goal of is to identify or quantify, or both, chemical components present in a given analyte, i.e., the sample under analysis. As recently discussed in [1], several tasks in AC keep some relationship to the broad classes of detection and estimation problems typically found in signal processing.

A Bayesian method for positive source separation

The paper considers the problem of source separation in the particular case where both the sources and the mixing coefficients are positive. The proposed method addresses the problem in a Bayesian framework. We assume a gamma distribution for the spectra and the mixing coefficients. This prior distribution enforces the non-negativity. This leads to an original method for positive source separation. A simulation example is presented to illustrate the effectiveness of the method.

On the use of ICA for hyperspectral image analysis

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.

Coronal Temperature Maps from Solar EUV Images: A Blind Source Separation Approach

Multi-wavelength solar images in the extreme ultraviolet (EUV) are routinely used for analysing solar features such as coronal holes, filaments, and flares. However, images taken in different bands often look remarkably similar, as each band receives contributions coming from regions with a range of different temperatures. This has motivated the search for empirical techniques that may unmix these contributions and concentrate salient morphological features of the corona in a smaller set of less redundant source images. Blind Source Separation (BSS) does precisely this. Here we show how this novel concept also provides new insight into the physics of the solar corona, using observations made by SDO/AIA. The source images are extracted using a Bayesian positive source-separation technique. We show how observations made in six spectral bands, corresponding to optically thin emissions, can be reconstructed by a linear combination of three sources. These sources have a narrower temperature response and allow for considerable data reduction, since the pertinent information from all six bands can be condensed into a single composite picture. In addition, they give access to empirical temperature maps of the corona. The limitations of the BSS technique and some applications are briefly discussed.

Application of Bayesian Non‐negative Source Separation to Mixture Analysis in Spectroscopy

In this paper we present an application of Bayesian non‐negative source separation to the analysis of spectral mixtures obtained from the analysis of multicomponent substances. The processing aims are formalized as a non‐negative source separation problem. The proposed Bayesian inference for the analysis is introduced and the main steps of the estimation algorithm are outlined. Some results obtained with simulated and experimental data are presented.

A variable structure observer for an on-line estimation of a tyre rolling resistance and effective radius

The rolling resistance and the effective radius of a tyre are two important characteristics that are very useful for vehicle diagnosis and wheel monitoring systems. This paper proposes to consider the physical model of rotational and longitudinal dynamics of the wheel and to apply a variable structure observer for an on-line estimation of these quantities using measurement of wheel angular velocity, vehicle speed and engine torque. These latter signals being available on major modern vehicle controller area networks (CAN), the proposed solution do not require any additional sensor. Experimental results are given in order to illustrate the relevance of this approach.

Efficiency of line search strategies in interior point methods for linearly constrained signal restoration

We discuss in this paper the influence of line search on the performances of interior point algorithms applied for constrained signal restoration. Interior point algorithms ensure the fulfillment of the constraints through the minimization of a criterion augmented with a barrier function. However, the presence of the barrier function can slow down the convergence of iterative descent algorithms when general-purpose line search procedures are employed. We recently proposed a line search algorithm, based on a majorization-minimization approach, which allows to handle the singularity introduced by the barrier function. We present here a comparative study of various line search strategies for the resolution of a sparse signal restoration problem with both primal and primal-dual interior point algorithms.

Entropy-Coded Lattice Vector Quantization Dedicated to the Block Mixture Densities

Entropy-coded lattice vector quantization (ECLVQ) with codebooks dedicated to independent identically distributed (i.i.d.) generalized Gaussian sources have proven their high coding performances in the wavelet domain. It is well known that wavelet coefficients with high magnitude (corresponding to edges and textures) tend to be clustered in a few amount of vectors. In this paper, we first show that this property has a major influence on the performances of ECLVQ schemes. Since this clustering property cannot be taken into account by the classical i.i.d. assumption, our first proposal is to model the joint distribution of vectors by a multidimensional mixture of generalized Gaussian (MMGG) densities. The main outcome of this MMGG model is to provide a theoretical framework to simply derive from i.i.d. - models, the corresponding MMGG - models. In a second part, a new codebook better suited to wavelet coding is proposed: the so-called dead zone lattice vector quantizers (DZLVQ). It consists of generalizing the scalar dead zone to vector quantization by thresholding vectors according to their energy. We show that DZLVQ improves the rate-distortion tradeoff. Experimental results are provided for the pyramidal LVQ scheme under the assumption of a multidimensional mixture of Laplacian (MML) densities. Results performed on a set of real life images show the precision of the analytical - curves and the efficiency of the DZLVQ scheme.

How to Apply ICA on Actual Data ? Example of Mars Hyperspectral Image Analysis

As any estimation method, results provided by ICA are dependent of a model - usually a linear mixture and separation model - and of a criterion - usually independence. In many actual problems, the model is a coarse approximation of the system physics and independence can be more or less satisfied, and consequently results are not reliable. Moreover, with many actual data, there is a lack of reliable knowledge on the sources to be extracted, and the interpretation of the independent components (IC) must be done very carefully, using partial prior information and with interactive discussions with experts. In this talk, we explain how such a scientific method can take place on the example of analysis of Mars hyperspectral images.