I have to do an exercise about the large deconvolution problem in astrophysics. First, we use the Moffat PSF to model atmospheric effects. Here's its expression :
I have generated a starting image from this PSF, but with adding white noise noise and background, like this :
Here's an example of starting image (30x30 pixels) :
Now, we consider the location of star and PSF parameters (r0,c0,alpha,beta) are known.
I have to answer to these questions :
For the first question, I am looking for the estimation of amplitude "a" of PSF and of value of background "b". I have to formulate the expression (1) under matricial form with a known matrix H and a set of data "d" (It seems that "d" array is the vector 1D expression of image 2D : d = D(:); and D = reshape(d,Rows,Columns).
So my question is : What is this expression with "known matrix H" ? I can't find in my courses this matricial expression that could allow to estimate the amplitude "a" of star and the estimation of "background" "b" ?
Which H known matrix is considered into this problem ?