Yes that is great to know. But where can I find an article that explains how exactly FT helps in my cell phone? What exactly do we do with FT in a cell phone?
So, how do you remove the high frequency parts? You apply a Fourier transform to the image (in this case, it's a "Discrete Cosine Transform", which is extremely similar to a DFT and has no differences for the purpose of this explanation) and get a 2d array. This 2d array has the low frequency parts in the upper left corner, and the high frequency parts everywhere else (to the right and down for horizontal and vertical frequencies). So your compression algorithm will simply zero out the high frequency parts so you don't have to store them. In the simplest case, this is equivalent to a simple blur of the image, but there are some heuristics about how much to remove (zero out) to minimize image degradation.
To decode the image, you take the 2d array and apply the inverse FT to get the original image (now slightly blurry because it's been compressed).
More details here: https://en.wikipedia.org/wiki/JPEG#Discrete_cosine_transform