How do I convert a Linux disk image into a sparse file?

First of all, sparse files are only handled transparently if you seek, not if you write zeroes.

To make it more clear, the example from Wikipedia

dd if=/dev/zero of=sparse-file bs=1k count=0 seek=5120

does not write any zeroes, it will open the output file, seek (jump over) 5MB and then write zero zeroes (i. e. nothing at all). This command (not from Wikipedia)

dd if=/dev/zero of=sparse-file bs=1k count=5120

will write 5MB of zeroes and will not create a sparse file!

As a consequence, a file that is already non-sparse will not magically become sparse later.

Second, to make a file with lots of zeroes sparse, you have to cp it

cp --sparse=always original sparsefile

or you can use tar's or rsync's --sparse option as well.

Perhaps the easiest way to sparsify a file in place would be to use fallocate utility as follows:

fallocate -v --dig-holes {file_name}

fallocate(1) is provided by util-linux package on Debian.

Do you mean that your ddrescue created image is, say, 50 GB and in reality something much less would suffice?

If that's the case, couldn't you just first create a new image with dd:

dd if=/dev/zero of=some_image.img bs=1M count=20000

and then create a filesystem in it:

mkfsofyourchoice some_image.img

then just mount the image, and copy everything from the old image to new one? Would that work for you?

PartImage can create disk images that only store the used blocks of a filesystem, thus drastically reducing the required space by ignoring unused block. I don't think you can directly mount the resulting images, but going:

image -> partimage -> image -> cp --sparse=alway

Should produce what you want (might even be possible to stick the last step, haven't tried).