Compressive sensing for spectroscopy and polarimetry

¹ Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife, Spain e-mail: aasensio@iac.es
² Departamento de Astrofísica, Universidad de La Laguna, 38205 La Laguna, Tenerife, Spain
³ THEMIS, CNRS UPS 853, c/vía Láctea s/n, 38200 La Laguna, Tenerife, Spain e-mail: arturo@themis.iac.es

Received: 30 July 2009
Accepted: 24 September 2009

Abstract

We demonstrate, through numerical simulations with real data, the feasibility of using compressive sensing techniques for the acquisition of spectro-polarimetric data. This allows us to combine the measurement and the compression process into one consistent framework. Signals are recovered using a sparse reconstruction scheme from projections of the signal of interest onto appropriately chosen vectors, typically noise-like vectors. The compressibility properties of spectral lines are analyzed in detail. The results shown in this paper demonstrate that, thanks to the compressibility properties of spectral lines, it is feasible to reconstruct the signals using only a small fraction of the information that is measured nowadays. We investigate in depth the quality of the reconstruction as a function of the amount of data measured and the influence of noise. This change of paradigm also allows us to define new instrumental strategies and to propose modifications to existing instruments in order to take advantage of compressive sensing techniques.