Scott W wrote:

In fact, it is relevant information, pure information, image
information.
Whereas you need additional information, irrelevant, non-image
information,
information about the compression algorithm, to compress and (more
importantly) decompress compressed information.

Let me give a very simple case, take a string of 1,000,000 1s, that
may be a lot of data, but very little information in all those 1s.

Let me explain another way.
How many bytes are used to store information is one thing.
Te thing however is that the value, the information content, in your example
above is 1,000,000. All 9 digits used to describe/hold that bit of
information indeed contain information.
You can perhaps use less storage to hold that same information (increase the
information per bit density), but the full "1,000,000" still is "information
content". Not something that remains, forms a "rest", besides "information
content".
;-)