MRA-Based Digital Filter Using Daubechies 12 and Deep Learning for Exoplanet Light Curves

The objective of this work is to remove systematic noise in transmission spectroscopy observations of exoplanets from the Earth's surface, using unsupervised clustering techniques and multiresolution analysis (MRA) based on the Daubechies 12 mother wavelet. This will allow training a neural network of NARX topology (Nonlinear Autoregressive Model with Exogenous Inputs), which will learn through the proposed method to remove the noise present in the observations. The approach proposes two ways of applying the NARX to remove the noise: first, by applying it to each observed wavelength and then recomposing the Light Curve; and second, by applying it directly on the Light Curve. The choice of the best method is based on the root mean square error (RMSE) metric, being of the order of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−7</sup> for the most efficient neural network obtained in this research.