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Sparse Representation of Multivalued Images: Application in Astrophysics

Final Report Summary - SPARSEASTRO (Sparse Representation of Multivalued Images: Application in Astrophysics)

The goals of this project was to i) develop tools for analyzing multi-valued astronomical data using sparsity, ii) create software packages which include these tools, and iii) use these tools in the framework of important astronomical international projects such as PLANCK, FERMI or EUCLID.
Sparsity is a recent field in applied mathematics and statistics, and the idea behind this concept is to project the data into a space where most of the information contained in the data can be compacted into few elements. This allows us to better detect the signal of interest and to use this information efficiently in different applications. Our first goal was therefore to derive new decompositions allowing us to handle multi-valued data set such as multichannel data or vector field. These new decompositions were then used to derived algorithms for data restoration, signal detection and statistical studies.
We have then applied our algorithms to real data such a WMAP or Planck data set, and we have shown that we were able to recover the famous three degree Kelvin light related the cosmic microwave background (CMB) much better than any other existing method. Then we made a statistical analysis of our map using again some of our new tools, and we have derived beautiful results on several scientific problems such the full consistency of Planck data with our standard cosmological model, the reconstruction of the primordial power spectrum or the detection of a very weak signature of the matter in the CMB, due to the passage of CMB photons through the gravitational potential (Integrated Sachs-Wolfe effect detection).
Another very nice achieved result is related to the reconstruction of the 3D density mass from gravitational shear measurements. We have shown that our method offer a very promising way of reconstructing the 3D density mass maps that outperforms significantly all existing methods. In particular, we have seen using simulations that we can reconstruct two clusters on the same light of sight, which was impossible with previous methods. We have also shown that this method is able to reconstruct both the density and redshift of dark matter halos with enough accuracy to put constraints on the halo masses.
Finally, all our software packages are be freely available through the SparseAstro web site, according to the reproducible research philosophy, which offers the possibility to any researcher to reproduce the results published in our papers.