i am working in digital image restoration field, recently i have studied image degradation model which is like that. g(x,y) = h(x,y)*f(x,y) + n(x,y)


g(x,y) is the degraded image

f(x,y) is the image that we wish to capture or its is latent image

h(x,y) is image degrading function, and * is convolution operator

n(x,y) is noise

my question is that, can i change this particular model like that.

g(x,y) = h(x,y)*{f(x,y)+n(x,y)}


2 Answers 2


In principle you can do that. You should, however, note that the two noise signals (both of which you called $n(x,y)$) are of course not identical. The two models are

$$g(x,y)=h(x,y)*f(x,y)+n(x,y)\\ g(x,y)=h(x,y)*\left[ f(x,y)+z(x,y)\right]$$

where the two noise components $n(x,y)$ and $z(x,y)$ have different properties. So you have to be careful with methods that assume certain noise properties. E.g. if it is assumed that $n(x,y)$ is white, then $z(x,y)$ is not white anymore and this has to be taken into account in the noise removal algorithm. The basic question you have to ask yourself is what you gain by changing the model.


they are equivalent in the sense that

$ g(x,y) = h(x,y)*{f(x,y)+n(x,y)} = h(x,y)*f(x,y) + h(x,y)*n(x,y)$

here $ h(x,y)*n(x,y) = N(x,y) $ is the new noise model and dependent on h(x,y). As far as I observe this will not simplify the signal estimation procedure because noise models are usually simpler in the initial model.


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