[amit_m]

Why go through the blurring, rescaling and JPEG compression?Simply take the first few DCT coefficients of the image, then quantize and compress them. In fact, one can make this scheme output the gaussian-blurred image by adding gaussian-weighted coefficient decay.

[ot]

What you are suggesting is absolutely not equivalent to gaussian blurring. Do low-quality JPEGs look nicely blurred to you?

Truncating the coefficients is a low-pass filter, which introduces nasty artifacts such as ringing. The transform of a gaussian is another gaussian, so you could in principle work in the frequency domain but only if the transform is applied to the whole image, while JPEG works in 8x8 blocks (as sp332 pointed out), and in any case there would be no computational benefit over applying the gaussian in the spatial domain.

[sp332]

Wouldn't that only work within a single JPEG block?