Pseudocode, since I don't have ImageMagick installed here.

# load original image (lena.jpg)
# get original image's geometry
# do
#    inflate dimensions by 1.2*
#    resize image to target geometry
#    add a little scatter noise to the image
#    set target quality to a high number like 99
#    save target image (lenna.jpg) to disk
# while (target image file size is too small);
[download]

The scatter noise and quality numbers are to frustrate jpeg's compression as the image grows.

Are we talking gigabytes of disk space? I think jpeg as a format will break at 2^15 (or maybe 2^16) pixel dimensions.