Re: JPEG compression only retains magnitude information? How about phase information?

Hi,

> I guess phase information is not useful at all, so JPEG just ignore them...

Not quite. A transform I would "ignore" information in case some information
is definitely lost. Lost in the sense that for a transform "I" there is
no inverse transformation "I^{-1}". Since DCT is completely reversible, not
a single bit of information is lost, and thus no kind of "phase" is lost 
either. Information gets lots only because a) you quantize and b) DCT is
implemented with limited precision. If a system had infinite computing
accuracy, DCT would be reversible.

> But is there any application that phase information can be useful?

Phase information of what? The relative phases of the light signal captured
as an image? That information is already lost at the time you take a photo,
unless it's a hologram.

> 1) How to get at the encoder side along with DCT coefficients magnitude
> information? and then it can be transmitted to the decoder side...

Make a hologram, digitialize it, then transmit this information. Classical
image compression algorithms might be unsuitable here because they might be
not precise enough/might be lossy for the wrong kind of the hologram.
(Kinna like: Image compression with gzip is possible, though not smart).

> 2) How to get at the decoder side by inferencing from DCT coefficient
> magnitude information, if they are not obtained at the encoder side and
> transmitted to the decoder side...

Again, there is no definite answer because there is no definite 
question. (-; Like in "The Hitchhiker's Guide Thru Galaxy", you first need
to find the proper question before getting the answer 42. (-;

So long,
        Thomas