An interpolation/extrapolation approach to X-ray imaging of solar flares

Silvia Allavena; Michele Piana; Federico Benvenuto; Anna Maria Massone

doi:10.3934/ipi.2012.6.147

Article Contents

2012, Volume 6, Issue 2: 147-162. Doi: 10.3934/ipi.2012.6.147

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An interpolation/extrapolation approach to X-ray imaging of solar flares

1.
Dipartimento di Matematica, Università di Genova, via Dodecaneso 35 16146 Genova
2.
CNR - Consiglio Nazionale delle Ricerche, SPIN, Genova, via Dodecaneso 33 16146 Genova

Received: November 30, 2010

Revised: September 30, 2011

Published: April 2012

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Abstract

We describe an interpolation/extrapolation procedure that reconstructs X-ray maps of solar flares using as input data sparse samples of the Fourier transform of the radiation flux, named visibilities. The algorithm is based on two steps: in the first step the performance of an interpolation routine is optimized by representing the visibilities according to favorable coordinates in the frequency plane. In the second step two extrapolation schemes are introduced, respectively based on the projection and the thresholding of the Landweber iterative method. The procedure is validated against realistic synthetic visibilities and applied to experimental measurements provided by the NASA satellite Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI).

Keywords:

X-ray solar imaging,
Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI),
visibilities,
iterative regularization methods,
soft thresholding.

Mathematics Subject Classification: Primary: 65J22, 68U10; Secondary: 65Z05.

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