Effect of noise on high and low frequency components

It is given that noise is present in the noisy image in the form of high frequency components. Can any one please explain this concept. Also please tell me that whether it is correct to say that "effect of white Gaussian noise is more on high frequency part of the image as compared to low frequency components" or not.

• I think there is a language problem here: "In theory it is given that noise is present in the noisy image in the form of high frequency components." Can you rephrase this and explain "it is given" ? I think the first answer below is probably the answer you want; but since I don't know the technical meaning of the question I can't be sure. For instance, you might have meant broadband, or out of, band noise leaking in; alternatively, you might have meant temporal edge time measurement. – rrogers Oct 5 '16 at 14:46

This is actually due to the characteristics of the actual signal, rather than noise.

You might have heard of pink noise and its spectral characteristics $$S(f)\propto \frac{1}{f^\alpha}$$ Now forget about the term "noise" in here, and imagine a stochastic process whose spectral density vanishes following a $\frac{1}{f^\alpha}$ law, in which $\alpha$ is a constant.

Interestingly, this is the law that nature follows a lot. More specifically, many natural signals follow this law. It has been observed and actually been verified to be valid for instance in human voice, natural images, music, quasar light emissions, heart beat, firings of neurons, and even in financial markets. Note that natural is a key term here and by that, we refer to attributes of a natural environment. For a more detailed discussion see here and here. For 2D (image) signals we should expect $\alpha=2$.

Since according to the $\frac{1}{f}$ law the contribution of the actual [natural] signal will diminish at higher frequencies, we would expect more contribution of noise at these frequencies. Consequently, noise is usually dominant at high frequencies and the signal is more dominant at lower frequencies.

• Schaaf and Hateren found that the spatial power spectra of their linear-intensity outdoor photos had on average $\alpha = 2$. They had almost always $1 < \alpha < 3$. Images that are composed of solid-color areas with well-defined edges will have $\alpha = 2$, because of the color discontinuity at the edges of the areas. – Olli Niemitalo May 2 '17 at 6:45
• Yes, $\alpha=2$ is just an approximation for natural images and is indeed case-specific, as you pointed out. – msm May 2 '17 at 7:28

effect of noise is more considerable in high frequency because it contain information(high) so any small noise is considerable...small noise even can change the whole information....on the other hand low frequency component contain small information over a large period and a small noise can't give much effect on it...

Additive noise (important to mention) will be added to the Fourier spectrum because the transform in question has the property that it is linear. And as msm mentions many signals in different fields have much more energy in the lower frequency bands than in the higher frequency bands, so the relative effect of the noise as compared to the signal energy will likely be larger for the higher frequencies.