Dealing with missing data: An inpainting application to the MICROSCOPE space mission

Abstract

Missing data are a common problem in experimental and observational physics. They can be caused by various sources, either an instrument's saturation, or a contamination from an external event, or a data loss. In particular, they can have a disastrous effect when one is seeking to characterize a colored-noise-dominated signal in Fourier space, since they create a spectral leakage that can artificially increase the noise. It is therefore important to either take them into account or to correct for them prior to e.g. a Least-Square fit of the signal to be characterized. In this paper, we present an application of the {\it inpainting} algorithm to mock MICROSCOPE data; {\it inpainting} is based on a sparsity assumption, and has already been used in various astrophysical contexts; MICROSCOPE is a French Space Agency mission, whose launch is expected in 2016, that aims to test the Weak Equivalence Principle down to the $10^{-15}$ level. We then explore the {\it inpainting} dependence on the number of gaps and the total fraction of missing values. We show that, in a worst-case scenario, after reconstructing missing values with {\it inpainting}, a Least-Square fit may allow us to significantly measure a $1.1\times 10^{-15}$ Equivalence Principle violation signal, which is sufficiently close to the MICROSCOPE requirements to implement {\it inpainting} in the official MICROSCOPE data processing and analysis pipeline. Together with the previously published KARMA method, {\it inpainting} will then allow us to independently characterize and cross-check an Equivalence Principle violation signal detection down to the $10^{-15}$ level.

Accepted for publication in Physical Review D. 12 pages, 6 figures

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Cited by in corpus (6)

• MICROSCOPE mission: final results of the test of the Equivalence Principle
• Space test of the Equivalence Principle: first results of the MICROSCOPE mission
• Gaussian regression and power spectral density estimation with missing data: The MICROSCOPE space mission as a case study
• Exponential shapelets: basis functions for data analysis of isolated features
• MICROSCOPE mission: Data analysis principle
• Dealing with missing data in the MICROSCOPE space mission: An adaptation of inpainting to handle colored-noise data