# American Institute of Mathematical Sciences

May  2012, 6(2): 147-162. doi: 10.3934/ipi.2012.6.147

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

 1 Dipartimento di Matematica, Università di Genova, via Dodecaneso 35 16146 Genova, Italy, Italy, Italy 2 CNR - Consiglio Nazionale delle Ricerche, SPIN, Genova, via Dodecaneso 33 16146 Genova, Italy

Received  December 2010 Revised  October 2011 Published  May 2012

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).
Citation: Silvia Allavena, Michele Piana, Federico Benvenuto, Anna Maria Massone. An interpolation/extrapolation approach to X-ray imaging of solar flares. Inverse Problems & Imaging, 2012, 6 (2) : 147-162. doi: 10.3934/ipi.2012.6.147
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