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I am trying to understand low pass filters for image processing, I came across an article that stated that low pass filters effect noise more than the real data due to that the image

Noise always changes rapidly from pixel to pixel because each pixel generates its own independent noise. The image from the telescope isn't "uncorrelated" in this fashion because real images are spread over many pixels.

Does this mean that the filter effects noise more due to the noise being correlated from pixel to pixel?

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Most images are inherently low-pass: the object that is displayed in the image generally doesn't change from pixel to pixel.

Most image pixel noise is generated by each individual pixel capturing the image. As a result this noise is generally assumed to be uncorrelated from pixel to pixel. That means the noise is (bandlimited) white noise, which has uniform components across all frequencies low to high.

So, when you apply a low pass filter to an image, most of the information about the objects imaged will pass straight through because they are in the low pass filter's pass band.

Conversely, noise will have its high frequency components attenuated by the low pass filter.

That is why the statement low pass filters effect noise more than the real data is generally true.

To answer your explicit question:

Does this mean that the filter effects noise more due to the noise being correlated from pixel to pixel?

The filter affects the noise more due to the noise being uncorrelated from pixel to pixel.

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    $\begingroup$ Excellent answer, thank you. The wording 'isn't uncorrelated' was a bit confusing. $\endgroup$
    – Colin747
    Jan 12, 2016 at 12:46
  • $\begingroup$ You're welcome! Yes, double negatives can be confusing, especially in technical writing. $\endgroup$
    – Peter K. ♦
    Jan 12, 2016 at 12:48

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