Re: D200 vs D300 at ISO 1600

On Fri, 11 Apr 2008 13:56:23 -0800, floyd@xxxxxxxxxx (Floyd L.
Davidson) wrote:

John O'Flaherty <quiasmox@xxxxxxxxx> wrote:
On Thu, 10 Apr 2008 19:02:48 -0800, floyd@xxxxxxxxxx (Floyd L.
Davidson) wrote:
If it is not a lossy compression, then someone kindly cite an example
where it compresses but the exact original signal can be recovered.

It is inherently a lossy compession.

As to nonlinear encodings, suppose you take the logarithm of a
digitized signal, to a precision much greater than the original
representation, and transmit mantissa changes continually, but
transmit the exponent only when it changes. That would be a nonlinear
compression, but would allow perfect recovery of the original signal.

First, that is not what we are referring to by
"non-linear encoding" compared to "linear encoding".
That is a totally different data rather than a different
encoding.

You've actually snipped out what "we" were referring to. You replied
to a statement that while jpeg encoding was lossy, some encodings
aren't lossy, and there are nonlinear encodings among the non-lossy
ones. You said that that compression is inherently lossy. What I cited
is an encoding, it's nonlinear, and it isn't lossy.

Regardless, it will not allow perfect recovery of the
original signal, for the same reason that one cannot
perfectly recover the original analog signal after it is
digitized. Quantization error, whether of the signal
itself or of the changes in the signal, will distort the
output compared to the input.

The input signal I specified was already quantized: "the logarithm of
a digitized signal".

It is only totally recoverable if you happen to have
infinite bandwidth, SNR, or time. See Claude Shannon's
"A Mathematical Theory of Communication", 1948.

I have read the book and have it at hand. If you can refer me to a
section number supporting some specific assertion you are making,
please do so. First, though, note that infinite resolution coding is
impossible, and there are no such things as infinite bandwidth, SNR,
or time, so the recovery you are talking about is a straw man.

If you refer to the compression of a digitized image, lossless
compression is very common.

Not due to non-linear encoding schemes it isn't!

We are *NOT* talking about whether data can be
compressed without loss. It can. But we are talking
about gamma-corrected encoding which compresses the data
to reduce bandwith by lowering the number of bits per
sample.

Your examples do not match the request.

Apparently, I answered what you said rather than what you meant, a
failing for which I can forgive myself. If you had made such a
carefully framed, limited statement to start with, I could have
answered more to your point. In any case, if the nonlinear encoding
maintains a distinction between adjacent levels which at all points is
smaller than the noise level at those points, it increases the
information transmitted in a given number of bits without loss of
anything but noise.

A simple example is: don't transmit or
store values that repeat n times, just use the value once along with
the number of repetitions (run length encoding).
Any digitized signal, which is necessarily already quantized, is a
set of numbers and can probably be compressed without loss by

You should have said "and might possibly be compressed"... :-)

Chances are.

algorithms that find patterns in the numbers. Once compressed by an
efficient routine, the signal can't be compressed further with the
same or another algorithm.

If you are starting with an unquantized signal that represents a real
number, you can't compress its magnitude without some loss (=
quantization), but if the losses are way less than the noise level,
nothing meaningful has been lost.

That is also a relatively useless accomplishment! In
fact practical quantization *always* involves data loss.
Again, as I've pointed out before: that *is*
quantization error.

You seem to be echoing what I said, but with added emphasis, as if
you were disagreeing with it. Digital cameras must quantize: it's what
they do for a living. And they must do so in a finite number of bits
to earn their keep. The question, then, is what kind of encoding will
maximize the accurate information that they record.
Upon further consideration, it appears to me that for a given fixed
number of bits, and using an encoding system without excess
redundancy, a nonlinear encoding will be more suited to a nonlinear
sensor recording wide ranging phenomena, and will carry more
information and be less lossy than a linear one.

--
John
.

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