Uncovering the Blurred Image: Finding K & f

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Homework Statement


I found that the blurred image is always presented by
$$A=Ku+f$$, where u is the perfect image source, and the K is transformation (blurring, sampling)
and f is the noising . The question I want to know is how can we find such K, or f when we blurred the image , for example ,using the gaussian blurring.
In other word, I want to know how can I find K or f s.t. I can do the same effect as using the
imnoise function in MATLAB as gaussian blurring or ...


Homework Equations


I found that there are matrix related to it, where the matrix is given by h=fspecial('gaussian',256);
and it is all zeros.


The Attempt at a Solution

 
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It's an inverse problem ... you need to use some regularization approach.
http://home.comcast.net/~szemengtan/InverseProblems/chap3.pdf
 
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um,, I just want to know how can I find such K and f...
Thanks you.:)
 
And I told you - use a regularization technique.
I'm not going to write out the 10-20 pages of theory here - hence the link.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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