Simultaneous analysis of large INTEGRAL/SPI11Based on observations with INTEGRAL, an ESA project with instruments and science data center funded by ESA member states (especially the PI countries: Denmark, France, Germany, Italy, Spain, and Switzerland), Czech Republic and Poland with participation of Russia and the USA. datasets: Optimizing the computation of the solution and its variance using sparse matrix algorithms

Abstract

Nowadays, analyzing and reducing the ever larger astronomical datasets is becoming a crucial challenge, especially for long cumulated observation times. The INTEGRAL/SPI X/γ-ray spectrometer is an instrument for which it is essential to process many exposures at the same time in order to increase the low signal-to-noise ratio of the weakest sources. In this context, the conventional methods for data reduction are inefficient and sometimes not feasible at all. Processing several years of data simultaneously requires computing not only the solution of a large system of equations, but also the associated uncertainties. We aim at reducing the computation time and the memory usage. Since the SPI transfer function is sparse, we have used some popular methods for the solution of large sparse linear systems; we briefly review these methods. We use the Multifrontal Massively Parallel Solver (MUMPS) to compute the solution of the system of equations. We also need to compute the variance of the solution, which amounts to computing selected entries of the inverse of the sparse matrix corresponding to our linear system. This can be achieved through one of the latest features of the MUMPS software that has been partly motivated by this work. In this paper we provide a brief presentation of this feature and evaluate its effectiveness on astrophysical problems requiring the processing of large datasets simultaneously, such as the study of the entire emission of the Galaxy. We used these algorithms to solve the large sparse systems arising from SPI data processing and to obtain both their solutions and the associated variances. In conclusion, thanks to these newly developed tools, processing large datasets arising from SPI is now feasible with both a reasonable execution time and a low memory usage.

Denoising, deconvolving, and decomposing photon observations

“…As an initial attempt, a maximum likelihood analysis was proposed by Valdes (1982). In later work, maximum entropy (Strong 2003) and minimum χ 2 methods (e.g., Bouchet et al 2013) were applied to the INTEGRAL/SPI data reconstructing a single signal component, though. On the basis of sparse regularization a number of techniques exploiting waveforms (based on the work by Haar 1910Haar , 1911 have proven successful in performing denoising and deconvolution tasks in different settings (González-Nuevo et al 2006;Willett & Nowak 2007;Dupe et al 2009;Figueiredo & Bioucas-Dias 2010;Dupé et al 2011).…”

Diffuse emission study with INTEGRAL/SPI: Results after 10 years of observations

“…We use the Cash [17] statistics, but we present the results in term of the equivalent chi-square statistics (χ 2 L ). The core algorithm developed to handle such a large system is described in [18]. The analysis performed in this paper will be described in more detailed in [19], we remind here the main points.…”