white noise in images For digital images, noise is assumed to be additive gaussian white noise. I remember noise in images is considered as high frequency. However, from the link
https://en.wikipedia.org/wiki/White_noise, it says 


  a random signal is considered "white noise" if it is observed to have
  a flat spectrum over the range of frequencies that is relevant to the
  context.


Does it mean frequencies of noise will extend from low frequencies to high frequencies? Why do we try to only remove high frequency component? Is human visual system  not sensitive to low frequency noise?

From the same link, https://en.wikipedia.org/wiki/White_noise


  In digital image processing, the pixels of a white noise image are
  typically arranged in a rectangular grid, and are assumed to be
  independent random variables with uniform probability distribution
  over some interval.


It reads that the pixels of a white noise image are assumed to be independent random variables with uniform probability distribution over some interval.
Does it mean that one pixel and its neighbors are i.i.d?
Yes, the noise is wide-band. 

A challenge in images resides in lowering the high-frequency noise components, while preserving the local high-frequency features of the contours and the textures, where you have fewer pixels to estimate a consistent denoised value. 

On low-frequency parts, the data is generally more regular or smooth, and getting rid of the noise is often performed more easily by averaging over neighboring pixels.