DS0705 - Fondements du numérique

Spectroscopic Decomposition in Multispectral Images – DSIM

Submission summary

Analysing the kinematics of the galaxy components is a key step for a better understanding of the universe, especially its history and evolution. Indeed, the Doppler effect induces the so-called redshift of the galaxy spectrum: this shift is a measure of the kinematics and, thus, allows to infer on the galaxy history. That is why recent telescopes provide multispectral images, that is 3D images whose third dimension corresponds to the wavelength. Each pixel in the images is a spectrum showing peaks whose parameters (wavelength, intensity, ...) provide the expected information.

The goal of the DSIM project is to develop image processing tools to decompose these spectra, i.e. to estimate the peak parameters as well as the peak number. This goal is facing several problems. First, the redshift yields a shift of the peaks in wavelength; the peaks are evolving in wavelength between two neighbouring pixels (but also in intensity and width). The evolution is slow through the multispectral image but has to be taken into account in the methods. Second, the avalanche of astronomical images provides huge data each night, requiring fast and efficient processing methods. Third, astronomical images usually suffer from very low signal-to-noise ratio since the acquired light is very low. Regarding these problems, we are convinced that taking benefits of the spatial redundancy is decisive to provide efficient methods.

A large number of studies are devoted to the decomposition of one spectrum, but the simultaneous decomposition of many spectra having strong relations is quite recent (source separation does not apply because the peaks evolve between two neighbouring pixels). Some approaches decompose the spectra independently of the neighbourhood, other approaches average spatial regions in the image. Clearly, no current approach is intended to the spectroscopic decomposition of multispectral images with a fine inclusion of the spatial information.

The spectroscopic decomposition is considered as an inverse problem. We assume that the peaks can be modelled as a parametric function with unknown parameters to recover. The slow spatial evolution is modelled using appropriate regularizations and priors. The first task aims at providing a very accurate decomposition. The problem is set in a Bayesian framework. Because the resulting solution space is huge and of unknown dimension, the use of RJMCMC and Hamiltonian MCMC algorithms seems to be of great interest. Besides, providing uncertainties on the estimation requires label switching methods dealing with a variable number of unknowns. The second task aims at exploring an alternative way so as to improve the computation time: we study the benefits of using sparse approximation methods. In this way, we propose regularization criteria to model the slow evolution. Considering the recent developments of structured sparsity, we also develop a method to estimate the groups from a particular dictionary (the atoms being a priori set since they have a physical meaning). The third task aims at testing the developed approaches on real astronomical images. Thus four astronomers associated on this project provide data and an expert feedback on the performances of the methods.

The DSIM project lies within former projects in which we have been involved. It provides significant progress in the modelling and the evolution of the peaks, as well as the development of efficient algorithms for manipulating these models, especially with MCMC algorithms and sparse approximation methods. Science return in the analysis of the galaxy kinematics is expected. The DSIM project produces also new tools for scientific communities using multispectral imaging and spectroscopy (e.g. biological or geological imaging).

Project coordination

Vincent Mazet (Laboratoire des Sciences de l'Ingénieur, de l'Informatique et de l'Image _ Université de Strasbourg)

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

ICube - UNISTRA Laboratoire des Sciences de l'Ingénieur, de l'Informatique et de l'Image _ Université de Strasbourg

Help of the ANR 183,024 euros
Beginning and duration of the scientific project: September 2014 - 48 Months

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