can i decompose image deblurring model? - Signal Processing Stack Exchange most recent 30 from dsp.stackexchange.com 2019-11-12T16:03:24Z https://dsp.stackexchange.com/feeds/question/9476 https://creativecommons.org/licenses/by-sa/4.0/rdf https://dsp.stackexchange.com/q/9476 0 can i decompose image deblurring model? Mayank Tiwari https://dsp.stackexchange.com/users/4444 2013-06-06T05:26:57Z 2013-06-06T10:42:07Z <p>i am working in digital image restoration field, recently i have studied image degradation model which is like that. <strong>g(x,y) = h(x,y)*f(x,y) + n(x,y)</strong></p> <p>where </p> <p><strong>g(x,y) is the degraded image</strong></p> <p><strong>f(x,y) is the image that we wish to capture or its is latent image</strong></p> <p><strong>h(x,y) is image degrading function, and * is convolution operator</strong></p> <p><strong>n(x,y) is noise</strong></p> <p>my question is that, can i change this particular model like that.</p> <p><strong>g(x,y) = h(x,y)*{f(x,y)+n(x,y)}</strong></p> https://dsp.stackexchange.com/questions/9476/-/9477#9477 3 Answer by Matt L. for can i decompose image deblurring model? Matt L. https://dsp.stackexchange.com/users/4298 2013-06-06T06:58:23Z 2013-06-06T06:58:23Z <p>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</p> <p>$$g(x,y)=h(x,y)*f(x,y)+n(x,y)\\ g(x,y)=h(x,y)*\left[ f(x,y)+z(x,y)\right]$$</p> <p>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.</p> https://dsp.stackexchange.com/questions/9476/-/9482#9482 0 Answer by RonaldoMessi for can i decompose image deblurring model? RonaldoMessi https://dsp.stackexchange.com/users/4737 2013-06-06T10:42:07Z 2013-06-06T10:42:07Z <p>they are equivalent in the sense that </p> <p>$g(x,y) = h(x,y)*{f(x,y)+n(x,y)} = h(x,y)*f(x,y) + h(x,y)*n(x,y)$</p> <p>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.</p>
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