Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing

TL;DR

This paper reviews the use of sparse representations like wavelets, ridgelets, and curvelets in astronomical data analysis, and discusses the impact of Compressed Sensing on data collection and image reconstruction.

Contribution

It provides a comprehensive overview of sparsity-based methods in astronomy and explores how Compressed Sensing influences data acquisition and processing.

Findings

Wavelets are widely used for filtering and detection in astronomy.

Sparse representations like ridgelets and curvelets help detect anisotropic features.

Compressed Sensing offers new possibilities for data sampling and image reconstruction.

Abstract

Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets or curvelets have also been proposed for the detection of anisotropic features such cosmic strings in the cosmic microwave background. We review in this paper a range of methods based on sparsity that have been proposed for astronomical data analysis. We also discuss what is the impact of Compressed Sensing, the new sampling theory, in astronomy for collecting the data, transferring them to the earth or reconstructing an image from incomplete measurements.