ISSI Visiting Scientists Programme


The process of image formation can be described by the integral equation [2]:

where g(x) is the recorded noisy image, f(y) is the original scene and K(x,y) is the so called Point Spread Function (PSF) of the imaging system. The effect of the PSF is called blurring  and it represents the image of a point source located at the point y (impulse response function).
If the PSF is space invariant (i.e. K(x,y)=K(x-y)), the image restoration problem becomes the deconvolution problem

Since RHESSI imaging system [3] has nine rotating collimators, characterized by nine different PSFs (and therefore by nine different resolutions and signal-to-noise ratios) the RHESSI imaging problem reduces to a multiple deconvolution problem, i.e., the problem of restoring an object using nine different images of it. Our idea is to address such problem taking into account the following methodological issues:

1.  instead of summing up the images and using an averaged PSF, a better resolution is achievable by appropriately combining the nine images and PSFs according to the approach followed in [4];

2.  a better accuracy is achievable by using a priori information on the solution (such as its positivity or its compact support [5]) and on the statistical properties of the noise affecting the data [1].


[1] Anconelli B., Bertero M., Boccacci P. and Carbillet M. 2005, Restoration of interferometric images IV: an algorithm for super-resolution of stellar systems, A&A (in press)

[2] Bertero M. and Boccacci P. 1998, Introduction to inverse problems in imaging, IOP, Bristol

[3] Hurford G. J. et al. 2002, The RHESSI Imaging Concept, Solar Physics  210, 61-86

[4] Piana M. and Bertero M. 1995, Regularized deconvolution of multiple images of the same object, J. Opt. Soc. Am. A  13, 1516-1523

[5] Piana M. and Bertero M. 1997, Projected Landweber method and preconditioning, Inverse Problems  13, 441-463





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