# newbie question on deadzone quantization

Started by August 30, 2005
```Hi,
Can some one help me with deadzone quantization. What is its
difference when compared to normal quantization methods?

I googled on it resulting unsatisfactory results :(

Is there a place on the web I can look for more information regarding
the same.

--
TIA,
jag

```
```Hi,

>  Can some one help me with deadzone quantization. What is its
> difference when compared to normal quantization methods?

There's no "normal" quantization, so to say. A quantizer is
a mapping from a continuous set A of "signals" to a discrete set "D"
of symbols such that every a in A is assigned a symbol d in D. A
dequantizer re-assigns every d a "representative" or "reconstruction value"
r in A. The pre-image of a symbol d is called a "bucket".

The "easiest" possible quantizer is the scalar equiquantizer: Here "A" is
the real line, and the buckets are intervals of a constant size \Delta,
for example:

(-3 Delta,-2 Delta], (-2 Delta, -Delta], (-Delta,0] (0,Delta] (Delta,2 Delta]...

Quantization is here simple: Divide the "signal" a by Delta, round to -infinity
and you get the symbol value:

0 -> 0
Delta/2 -> 0
-Delta/2 -> -1
3.5 * Delta -> 3

etc.

A "scalar equiquantizer with deadzone" works very similar, the only difference
is that the size of the bucket containing the zero-signal has a different
size, say Theta. Here is a typical example for an equiquantizer with
deadzone with Theta = 2 Delta:

(-3 Delta,-2 Delta], (-2 Delta, -Delta], (-Delta,Delta] (Delta,2 Delta], (2 Delta,3 Delta]

(Note the difference above).

It is often a good idea to introduce a deadzone because a lot of noise is then
quantized to zero.

A scalar equiquantizer is found in traditional JPEG-1, equiquantizers with
deadzone are found in JPEG2000 (as above here Theta = 2 * Delta), scalar
equiquantizers with arbitrary deadzone are in JPEG2000-2. Then, we can also
consider quantizers where the symbol set A is not the real line, but a higher-
dimensional space. These are called "vector quantizers". One nice vector
quantizer is the Trellis Quantizer (TCQ) in JPEG2000-2.

> I googled on it resulting unsatisfactory results :(

Recommended reading on quantizers:

Robert M. Gray, David L. Neuhoff:
Quantization
IEEE Transactions on Information Theory, Vol. 44, No. 6, October 1998

So long,
Thomas
```