Separation of parameterized and delayed sources : application to spectroscopic and multispectral data

Abstract : This work is motivated by photoelectron spectroscopy and the study of galaxy kinematics where data respectively correspond to a temporal sequence of spectra and a multispectral image. The objective is to estimate the characteristics (amplitude, spectral position and shape) of peaks embedded in the spectra, but also their evolution within the data. In the considered applications, this evolution is slow since two neighbor spectra are often very similar: this a priori knowledge that will be taken into account in the developed methods. This inverse problem is approached as a delayed source separation problem where spectra and peaks are respectively associated with mixtures and sources. The state-of-the-art methods are inadequate because they suppose the source decorrelation and independence, which is not the case. We take advantage of the source knowledge in order to model them by a parameterized function. We first propose an alternating least squares method: the shape parameters are estimated with the Levenberg-Marquardt algorithm, whilst the amplitudes and positions are estimated with an algorithm inspired from Orthogonal Matching Pursuit. A second method introduces a regularization term to consider the delay slow evolution; a new joint sparse approximation algorithm is thus proposed. Finally, a third method constrains the evolution of the amplitudes, positions and shape parameters by B-spline functions to guarantee their slow evolution. The B-spline control points are estimated with a non-linear least squares algorithm. The results on synthetic and real data show that the proposed methods are more effective than state-of-the-art methods and as effective as a Bayesian method which is adapted to the problem. Moreover, the proposed methods are significantly faster.
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Submitted on : Friday, July 12, 2019 - 12:48:06 PM
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Hassan Mortada. Separation of parameterized and delayed sources : application to spectroscopic and multispectral data. Signal and Image processing. Université de Strasbourg, 2018. English. ⟨NNT : 2018STRAD051⟩. ⟨tel-02181704⟩

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