Mathematical Tools for Instrumentation & Signal Processing in Astronomy

This book is a collection of 13 articles corresponding to lectures and research works exposed at the Summer school of the CNRS titled « Bases mathématiques pour l’instrumentation et le traitement du signal en astronomie ». The school took place in Nice and Porquerolles, France, from June 1 to 5, 2015.

This book contains three parts:

I. Astronomy in the coming decade and beyond

The three chapters of this part emphasize the strong interdisciplinary nature of Astrophysics, both at theoretical and observational levels, and the increasingly larger sizes of data sets produced by increasingly more complex instruments and infrastructures. These remarkable features call in the same time for more mathematical tools in signal processing and instrumentation, in particular in statistical modeling, large scale inference, data mining, machine learning, and for efficient processing solutions allowing their implementation.

II. Mathematical concepts, methods and tools

The first chapter of this part starts with an example of how pure mathematics can lead to new instrumental concepts, in this case for exoplanet detection. The four other chapters of this part provide a detailed introduction to four main topics: Orthogonal functions as a powerful tool for modeling signals and images, covering Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals and Spherical Harmonic series for 2D signals; Optimization and machine learning methods with application to inverse problems, denoising and classication, with on-line numerical experiments; Large scale statistical inference with adaptive procedures allowing to control the False Discovery Rate, like the Benjamini-Hochberg procedure, its Bayesian interpretation and some variations; Processing solutions for large data sets, covering the Hadoop framework and YARN, the main tools for the management of both the storage and computing capacities of a cluster of machines and also recent solutions like Spark.

III. Application: tools in action

This parts collects a number of current research works where some tools above are presented in action: optimization for deconvolution, statistical modeling, multiple testing, optical and instrumental models. The applications of this part include astronomical imaging, detection and estimation of circumgalactic structures, and detection of exoplanets.

Slides and numerical experiments can be found at https://basmati.oca.eu.