ALGORITHM

The main blind deconvolution algorithm used here for restoration of SXT data and PSF is described in (Ayers, Dainty, 1988).  Before the deconvolution process can be run, an initial approximation of the PSF p0and SXT data d need to be prepared.  Initial PSF p0 is constructed by Steepest Descent Method. Data d must decompressed background substracted and converted to photon counts.
Both d and p0 are expected to be positive. PSF initial approximation is also reguired to be normalized to unit integral.

Then, the followings steps are iteratively repeated:

1)   Take the Fourier transform  P1of p1  (at the first iteration  p1 = p)
2)   Find approximation of Fourier transform of SXT image I1 = D /P1, where D is Forurier transform of d
3)   Conctruct deblured SXT image i1 by inverse Fourier transform of I1 
4)   Make a new image i2 by imposing positivity and total count conservation constraints on i 
5)   Take the Fourier transform  I2of i2 
6)   Find approximation of Fourier transform of SXT PSF P2 = D /I2, where D is Forurier transform of d
7)   Conctruct PSF approximation  p2 by inverse Fourier transform of P2 
8)   Make a new  p1 by imposing positivity and normalization to unity constraints on p2 . Close the blind deconvolution loop in this way.

Before the step 6 is performed above, additional averaging of Fourier transforms of image  I1 and  I2 is made.