Charles Soussen

Most methods for sparse signal recovery require setting one or several hyperparameters. We propose an unsupervised method to estimate the parameters of a Bernoulli-Gaussian (BG) model describing sparse signals. The proposed method is first derived for denoising problems using a maximum likelihood (ML) approach. Then, an extension to general inverse problems is achieved through a latent variable formulation. Two expectation-maximization (EM) algorithms are then proposed to estimate the signal together with the BG model parameters. Combining these two approaches leads to the proposed LEMUR algorithm. LEMUR is then evaluated on extensive simulations regarding the ability to recover the parameters and provide accurate sparse signal estimates.

Accepté à la conférence EUSIPCO 2024

Accepté à la conférence EUSIPCO 2024

Reflectance spectroscopy is a widely used technique for mineral identification and characterization. Since modern airborne and satellite-borne sensors yield an increasing number of hyperspectral data, it is crucial to develop unsupervised methods to retrieve relevant spectral features from reflectance spectra. Spectral deconvolution aims to decompose a reflectance spectrum as a sum of a continuum modeling its overall shape and some absorption features. We present a flexible and automatic method able to deal with various minerals. The approach is based on a physical model and allows us to include noise statistics. It consists of three successive steps: (i) continuum pre-estimation based on non-linear least-squares; (ii) pre-estimation of absorption features using a greedy algorithm; (iii) refinement of the continuum and absorption estimates. The procedure is first validated on synthetic spectra, including a sensitivity study to instrumental noise and a comparison to other approaches. Then, it is tested on various laboratory spectra. In most cases, absorption positions are recovered with an accuracy lower than 5 nm, enabling mineral identification. Finally, the proposed method is assessed using hyperspectral images of quarries acquired during a dedicated airborne campaign. Minerals such as calcite and gypsum are accurately identified based on their diagnostic absorption features, including when they are in a mixture. Small changes in the shape of the kaolinite doublet are also detected and could be related to crystallinity or mixtures with other minerals such as gibbsite. The potential of the method to produce mineral maps is also demonstrated.

Context. Extracting the multiphase structure of the neutral interstellar medium is key to understanding star formation in galaxies. The radiative condensation of the diffuse warm neutral medium producing a thermally unstable lukewarm medium and a dense cold medium is closely related to the initial step leading the atomic-to-molecular (HI-to-H₂) transition and the formation of molecular clouds. Up to now, the mapping of these phases out of 21 cm emission hyper-spectral cubes has remained elusive mostly due to the velocity blending of individual cold structures present on a given line of sight. As a result, most of the current knowledge about the HI phases rests on a small number of absorption measurements on lines of sight crossing radio sources. Aims. The goal of this work is to develop a new algorithm to perform separation of diffuse sources in hyper-spectral data. Specifically the algorithm was designed in order to address the velocity blending problem by taking advantage of the spatial coherence of the individual sources. The main scientific driver of this effort was to extract the multiphase structure of the HI from 21 cm line emission only, providing a means to map each phase separately, but the algorithm developed here should be generic enough to extract diffuse structures in any hyper-spectral cube. Methods. We developed a new Gaussian decomposition algorithm named ROHSA based on a multi-resolution process from coarse to fine grid. ROHSA uses a regularized nonlinear least-square criterion to take into account the spatial coherence of the emission and the multiphase nature of the gas simultaneously. In order to obtain a solution with spatially smooth parameters, the optimization is performed on the whole data cube at once. The performances of ROHSA were tested on a synthetic observation computed from numerical simulations of thermally bi-stable turbulence. We apply ROHSA to a 21 cm observation of a region of high Galactic latitude from the GHIGLS survey and present our findings. Results. The evaluation of ROHSA on synthetic 21 cm observations shows that it is able to recover the multiphase nature of the HI. For each phase, the power spectra of the column density and centroid velocity are well recovered. More generally, this test reveals that a Gaussian decomposition of HI emission is able to recover physically meaningful information about the underlying three-dimensional fields (density, velocity, and temperature). The application on a real 21 cm observation of a field of high Galactic latitude produces a picture of the multiphase HI, with isolated, filamentary, and narrow (σ ~ 1−2 km s⁻¹) structures, and broader (σ ~ 4−10 km s⁻¹), diffuse, and space-filling components. The test-case field used here contains significant intermediate-velocity clouds that were well mapped out by the algorithm. As ROHSA is designed to extract spatially coherent components, it performs well at projecting out the noise. Conclusions. In this paper we introduce ROHSA, a new algorithm that performs a separation of diffuse sources in hyper-spectral data on the basis of a Gaussian decomposition. The algorithm makes no assumption about the nature of the sources, except that each one has a similar line width. The tests we made shows that ROHSA is well suited to decomposing complex 21 cm line emission of regions of high Galactic latitude, but its design is general enough that it could be applied to any hyper-spectral data type for which a Gaussian model is relevant.

Spatially resolved multiply excited autofluorescence spectroscopy is a valuable optical biopsy technique to investigate skin UV-Visible optical properties in vivo in clinics. However, it provides bulk fluorescence signals from which the individual endogenous fluorophore contributions need to be disentangled. Skin optical clearing allows for increasing tissue transparency, thus providing access to more accurate in-depth information. The aim of the present contribution was to study the time changes in skin spatially resolved and multiply excited autofluorescence spectra during skin optical clearing. The latter spectra were acquired on an ex vivo human skin strip lying on a fluorescent gel substrate during 37 minutes of the optical clearing process of a topically applied sucrose-based solution. A Non Negative Matrix Factorization-based blind source separation approach was proposed to unmix skin tissue intrinsic fluorophore contributions and to analyze the time evolution of this mixing throughout the optical clearing process. This spectral unmixing exploited the multidimensionality of the acquired data, i.e., spectra resolved in five excitation wavelengths, four source-to-detector separations, and eight measurement times. Best fitting results between experimental and estimated spectra were obtained for optimal numbers of 3 and 4 sources. These estimated spectral sources exhibited common identifiable shapes of fluorescence emission spectra related to the fluorescent gel substrate and to known skin intrinsic fluorophores matching namely dermis collagen/elastin and epidermis flavins. The time analysis of the fluorophore contributions allowed us to highlight how the clearing process towards the deepest skin layers impacts skin autofluorescence through time, namely with a strongest contribution to the bulk autofluorescence signal of dermis collagen (respectively epidermis flavins) fluorescence at shortest (respectively longest) excitation wavelengths and longest (respectively shortest) source-to-detector separations.

Piecewise signals appear in many application fields. Here, we propose a framework for segmenting such signals based on the modeling of each piece using a parametric probability distribution. The proposed framework first models the segmentation as an optimization problem with sparsity regularization. Then, an algorithm based on dynamic programming is utilized for finding the optimal solution. However, dynamic programming often suffers from a heavy computational burden. Therefore, we further show that the proposed framework is parallelizable and propose using GPU-based parallel computing to accelerate the computation. This approach is highly desirable for the analysis of large volumes of data which are ubiquitous. Experiments on both simulated and real genomic datasets from next generation sequencing demonstrate improved performance in terms of both segmentation quality and computational speed.