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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, Italy, Italy, Italy |
2. | CNR - Consiglio Nazionale delle Ricerche, SPIN, Genova, via Dodecaneso 33 16146 Genova, Italy |
References:
[1] |
M. J. Aschwanden, E. Schmal and the RHESSI Team, Reconstruction of RHESSI solar flare images with a forward-fitting method, Solar Phys., 210 (2002), 193-211.
doi: 10.1023/A:1022469811115. |
[2] |
H. Bialy, Iterative behandlung linearer funktionalgleichungen, Arch. Rat. Mech. Anal., 4 (1959), 166-176.
doi: 10.1007/BF00281385. |
[3] |
F. L. Bookstein, Principal warps: Thin-plate splines and the decomposition of deformations, IEEE Trans. Pattern Anal. Mach. Int., 11 (1989), 567-585.
doi: 10.1109/34.24792. |
[4] |
S. C. Bong, L. Jeongwoo, D. E. Gary and H. S. Yun, Spatio-spectral maximum entropy method. I. Formulation and test, Astrophys. J., 636 (2006), 1159-1165.
doi: 10.1086/498225. |
[5] |
T. F. Chan and L. A. Vese, Active contours without edges, IEEE Trans. Im. Proc., 10 (1997), 266-277.
doi: 10.1109/83.902291. |
[6] |
D. L. Donoho, Superresolution via sparsity constraints, SIAM J. Math. Anal., 23 (1992), 1309-1331.
doi: 10.1137/0523074. |
[7] |
I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math., 57 (2004), 1413-1457.
doi: 10.1002/cpa.20042. |
[8] |
R. W. Gerchberg, Super-resolution through error energy reduction, Optical Acta, 21 (1974), 709-720.
doi: 10.1080/713818946. |
[9] |
G. J. Hurford, et al., The RHESSI imaging concept, Solar Phys., 210 (2002), 61-90.
doi: 10.1023/A:1022436213688. |
[10] |
E. P. Kontar, I. G. Hannah, N. L. S. Jeffrey and M. Battaglia, The sub-arcsecond hard X-ray structure of loop footpoints in a solar flare, Astrophys. J., 717 (2010), 250.
doi: 10.1088/0004-637X/717/1/250. |
[11] |
R. Lagendijk, J. Biemond and D. Boekee, Regularized iterative image restoration with ringing reduction, IEEE Trans. Acoust. Speech Signal Process., 36 (1988), 1874.
doi: 10.1109/29.9032. |
[12] |
R. P. Lin, et al., The Reuven Ramaty high-energy solar spectroscopic imager, Solar Phys., 210 (2002), 3-32. |
[13] |
A. M. Massone, A. G. Emslie, G. J. Hurford, M. Prato, E. P. Kontar and M. Piana, Hard X-ray imaging of solar flares using interpolated visibilities, Astrophys. J., 703 (2009), 2004-2016.
doi: 10.1088/0004-637X/703/2/2004. |
[14] |
M. Piana and M. Bertero, Projected Landweber method and preconditioning, Inverse Problems, 13 (1997), 441-463.
doi: 10.1088/0266-5611/13/2/016. |
[15] |
Marco Prato, A. Gordon Emslie, Eduard P. Kontar, Anna Maria Massone and Michele Piana, The location of centroids in photon and electron maps of solar flares,, Astrophys. J., 706 ().
|
[16] |
E. J. Schmahl, R. L. Pernak, G. J. Hurford, J. Lee and S. Bong, Analysis of RHESSI flares using a radio astronomical technique, Solar Phys., 240 (2007), 242-252.
doi: 10.1007/s11207-007-0263-1. |
[17] |
A. R. Thompson, J. M. Moran and G. W. Swenson, "Interferometry and Synthesis in Radioastronomy," Wiley, 2004. |
[18] |
A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov and A. Yagola, "Numerical Methods for the Solution of Ill-posed Problems," Translated from the 1990 Russian original by R. A. M. Hoksbergen and revised by the authors, Mathematics and its Applications, 328, Kluwer Academic Publishers Group, Dordrecht, 1995. |
show all references
References:
[1] |
M. J. Aschwanden, E. Schmal and the RHESSI Team, Reconstruction of RHESSI solar flare images with a forward-fitting method, Solar Phys., 210 (2002), 193-211.
doi: 10.1023/A:1022469811115. |
[2] |
H. Bialy, Iterative behandlung linearer funktionalgleichungen, Arch. Rat. Mech. Anal., 4 (1959), 166-176.
doi: 10.1007/BF00281385. |
[3] |
F. L. Bookstein, Principal warps: Thin-plate splines and the decomposition of deformations, IEEE Trans. Pattern Anal. Mach. Int., 11 (1989), 567-585.
doi: 10.1109/34.24792. |
[4] |
S. C. Bong, L. Jeongwoo, D. E. Gary and H. S. Yun, Spatio-spectral maximum entropy method. I. Formulation and test, Astrophys. J., 636 (2006), 1159-1165.
doi: 10.1086/498225. |
[5] |
T. F. Chan and L. A. Vese, Active contours without edges, IEEE Trans. Im. Proc., 10 (1997), 266-277.
doi: 10.1109/83.902291. |
[6] |
D. L. Donoho, Superresolution via sparsity constraints, SIAM J. Math. Anal., 23 (1992), 1309-1331.
doi: 10.1137/0523074. |
[7] |
I. Daubechies, M. Defrise and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math., 57 (2004), 1413-1457.
doi: 10.1002/cpa.20042. |
[8] |
R. W. Gerchberg, Super-resolution through error energy reduction, Optical Acta, 21 (1974), 709-720.
doi: 10.1080/713818946. |
[9] |
G. J. Hurford, et al., The RHESSI imaging concept, Solar Phys., 210 (2002), 61-90.
doi: 10.1023/A:1022436213688. |
[10] |
E. P. Kontar, I. G. Hannah, N. L. S. Jeffrey and M. Battaglia, The sub-arcsecond hard X-ray structure of loop footpoints in a solar flare, Astrophys. J., 717 (2010), 250.
doi: 10.1088/0004-637X/717/1/250. |
[11] |
R. Lagendijk, J. Biemond and D. Boekee, Regularized iterative image restoration with ringing reduction, IEEE Trans. Acoust. Speech Signal Process., 36 (1988), 1874.
doi: 10.1109/29.9032. |
[12] |
R. P. Lin, et al., The Reuven Ramaty high-energy solar spectroscopic imager, Solar Phys., 210 (2002), 3-32. |
[13] |
A. M. Massone, A. G. Emslie, G. J. Hurford, M. Prato, E. P. Kontar and M. Piana, Hard X-ray imaging of solar flares using interpolated visibilities, Astrophys. J., 703 (2009), 2004-2016.
doi: 10.1088/0004-637X/703/2/2004. |
[14] |
M. Piana and M. Bertero, Projected Landweber method and preconditioning, Inverse Problems, 13 (1997), 441-463.
doi: 10.1088/0266-5611/13/2/016. |
[15] |
Marco Prato, A. Gordon Emslie, Eduard P. Kontar, Anna Maria Massone and Michele Piana, The location of centroids in photon and electron maps of solar flares,, Astrophys. J., 706 ().
|
[16] |
E. J. Schmahl, R. L. Pernak, G. J. Hurford, J. Lee and S. Bong, Analysis of RHESSI flares using a radio astronomical technique, Solar Phys., 240 (2007), 242-252.
doi: 10.1007/s11207-007-0263-1. |
[17] |
A. R. Thompson, J. M. Moran and G. W. Swenson, "Interferometry and Synthesis in Radioastronomy," Wiley, 2004. |
[18] |
A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov and A. Yagola, "Numerical Methods for the Solution of Ill-posed Problems," Translated from the 1990 Russian original by R. A. M. Hoksbergen and revised by the authors, Mathematics and its Applications, 328, Kluwer Academic Publishers Group, Dordrecht, 1995. |
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