General :: Filesystems - Convert A Disk Image Into A Sparse File?

I have a bunch of disk images, made with ddrescue, on an EXT partition, and I want to reduce their size without losing data, while still being mountable. How can I fill the empty space in the image's filesystem with zeros, and then convert the file into a sparse file so this empty space is not actually stored on disk?

For example:

> du -s --si --apparent-size Jimage.image
120G Jimage.image
> du -s --si Jimage.image
121G Jimage.image

This actually only has 50G of real data on it, though, so the second measurement should be much smaller.

This supposedly will fill empty space with zeros: cat /dev/zero > zero.file rm zero.file But if sparse files are handled transparently, it might actually create a sparse file without writing anything to the virtual disk, ironically preventing me from turning the virtual disk image into a sparse file itself. :) Does it? Note: For some reason, sudo dd if=/dev/zero of=./zero.file works when cat does not on a mounted disk image.