Authors: | S. Pires |

Language: | IDL |

Download: | K-Inpainting.tar |

Description: | An IDL inpainting code for asteroseismology |

Notes: | Requires iSAP installation |

See the **IRFU/DAp software page** for more details.

The MICROSCOPE space mission, launched on April 25, 2016, aims to test the weak equivalence principle (WEP) with a 10^{15} precision. To reach this performance requires an accurate and robust data analysis method, especially since the possible WEP violation signal will be dominated by a strongly colored noise. An important complication is brought by the fact that some values will be missing –therefore, the measured time series will not be strictly regularly sampled. Those missing values induce a spectral leakage that significantly increases the noise in Fourier space, where the WEP violation signal is looked for, thereby complicating scientific returns.

Recently, we developed an inpainting algorithm to correct the MICROSCOPE data for missing values (in red, fig 4). This code has been integrated in the official MICROSCOPE data processing and analysis pipeline because it enables us to significantly measure an equivalence principle violation (EPV) signal in a model-independent way, in the inertial satellite configuration. In this work, we present several improvements to the method that may allow us now to reach the MICROSCOPE requirements for both inertial and spin satellite configurations (green curve, fig. 4).

The code corresponding to the paper is available for download here.

Although, the inpainting method presented in this paper has been optimized to the MICROSCOPE data, it remains sufficiently general to be used in the general context of missing data in time series dominated by an unknown colored-noise.

Dealing with missing data in the MICROSCOPE space mission: An adaptation of *inpainting* to handle colored-noise data, S. Pires, J. Bergé, Q. Baghi, P. Touboul, G. Métris, accepted in Physical Review D, December 2016

Dealing with missing data: An inpainting application to the MICROSCOPE space mission, J. Bergé, S. Pires, Q. Baghi, P. Touboul, G. Metris, Physical Review D, 92, 11, December 2015

MOOC on “Representations Parcimonieuses des Données, Des Particules aux Etoiles” by Sandrine Pires given at Doctoral school PHENIICS of Paris-Saclay

MOOC on “Débruitage par Des Méthodes Parcimonieuses, Des Particules aux Etoiles” by Sandrine Pires given at Doctoral school PHENIICS of Paris-Saclay

MOOC on “Interpolation des Données Manquantes par des Méthodes Parcimonieuses” by Sandrine Pires given at Doctoral school PHENIICS of Paris-Saclay

Title : Sparse decompositions for advanced data analysis of hyperspectral data in biological applications

*Abstract : Blind source separation aims at extracting unknown source signals from observations where these sources are mixed together by an unknown process. However, this very generic and non-supervised approach does not always provide exploitable results. Therefore, it is often necessary to add more constraints, generally arising from physical considerations, in order to favor the recovery of sources with a particular sought-after structure. Non-negative matrix factorization (NMF), which is the main focus of this thesis, aims at searching for non-negative sources which are observed through non-negative linear mixtures.*

*In some cases, further information still remains necessary in order to correctly separate the sources. Here, we focus on the sparsity concept, which helps improving the contrast between the sources, while providing very robust approaches, even when the data are contaminated by noise. We show that in order to obtain stable solutions, the non-negativity and sparse constraints must be applied adequately. In addition, using sparsity in a potentially redundant transformed domain could allow to capture the structure of most of natural image, but this kind of regularization proves difficult to apply together with the non-negativity constraint in the direct domain. We therefore propose a sparse NMF algorithm, named nGMCA (non-negative Generalized Morphological Component Analysis), which overcomes these difficulties by making use of proximal calculus techniques. Experiments on simulated data show that this algorithm is robust to additive Gaussian noise contamination, with an automatic control of the sparsity parameter. This novel algorithm also proves to be more efficient and robust than other state-of-the-art NMF algorithms on realistic data.*

*Finally, we apply nGMCA on liquid chromatography – mass spectrometry data. Observation of these data show that they are contaminated by multiplicative noise, which greatly deteriorates the results of the NMF algorithms. An extension of nGMCA was designed to take into account this type of noise, thanks to the use of a non-stationary prior. This extension is then able to obtain excellent results on annotated real data.*