Averaging the Random Noise

For this example a photo was scanned using a Mustek 12000P ScanExpress 36-bit scanner. Up to 8 images were successively acquired at Contrast=0, Brightness=0, Gamma=1 and with 300 DPI.  Btw: the photo shows one of our birds, Tipi. Usually he is sitting on my shoulder or the edge of the monitor watching carefully what is happening, and believe it or not he actually has done an incremental backup once on my system, by stepping over and beacking the unattended keyboard when the Windows desktop and it's icon were displayed.

Overview: size scaled down to 25%, otherwise not edited, compensated for gamma 2.2 viewing

About the noise

CCD acquire devices can have mainly three types of noise: 

Random noise. This is usually called thermal- or white noise and has uniform distribution over the frequency or normal or gaussian distribution over levels. It is the result of electron motion and recombination.

Dark-current noise. This is systematic noise (actually leakage current) that is rather constant at given ambient temperature. dark-current noise can be subtracted away from a captured image by taking a dark field image just before or after the actual image. Dark-current noise is only a problem at long exposure times. The dark current noise doubles with each 7C ... 10 C degree rise of ambient temperature. Only a few cameras actually do the black field subtraction.

Interference pick-up. This is usually a result of inefficient shielding (of either the device in concern or the disturbing device). In photographic imaging interference is seen usually as (somewhat) repeating patterns.

The technique

The photo was scanned 8 times successively, resulting images were arranged into layers in Photoshop and layers were combined by setting the opacity value in normal mode as follows: (see Revised Layer Summing below)

8th scan - layer 8 opacity = 12% 
7th scan - layer 7 opacity = 14% 
6th scan - layer 6 opacity = 17% 
5th scan - layer 5 opacity = 20% 
4th scan - layer 4 opacity = 25% 
3rd scan - layer 3 opacity = 33% 
2nd scan - layer 2 opacity = 50% 
1st scan - layer 1 opacity = 100% 

This technique will average the random noise while keeping the image information intact. Adding even more scans to the composition will improve the quality, the opacity values are 100% / layer#. 

Note that the scanner may have 1 or 2 bit offset from scan to scan so the layers may need positioning. This can be done in Photoshop by comparing the each of the layers in difference mode, separately between the background and by nudging the layer so that the difference view appears as black as possible.

Is it Worth the Trouble

Below the framed area (un-edited raw scans, but compensated for gamma 2.2 viewing and saved to jpeg at quality 6 in Photoshop) is shown at 400% zoom in three situations. 

Picture 1: Only layer 1 active.

Picture 1 shows very bad noise in deep shadows, but also e.g. the beak and the gray wall on the left are noisy.

Picture 2: Layers 1...4 active.

In picture 2 four layers are averaged and noticeably some of the noise is cleaned away.

Picture 3 shows even less noise but still the deep shadows are rather bad. The outline of the beak appears more smooth than in picture 2 and 1. Notice the improvement in the appearance of the nostril too.

 Conclusions

Averaging technique is easily possible using a scanner, each scan was exactly positioned, no adjustments were required. 

A clear improvement was achieved, that is very beneficial for the further editing.

The particular scanner is very noisy, incidentally it had no noise specifications.

In order to meaningfully claim a 36-bit performance (12-bit/color) the noise level should be about half of the LSB (least significant bit) and preferable much less. That would be the same as signal to noise ratio of:

20*log(2^12) + 3dB = 75.2dB or better.

An 8-bit/color system should have S/N ratio equal or better than 51 dB. 

In case the system had such a good S/N ratio the above technique would not have a lot of effect, there would not be any/much noise to average in the first place.

It is a good practice to keep the the noise figure (signal to noise ratio) as a major purchase criteria when buying a scanner or a digital camera. An 8-bit/color device with 51 dB S/N is just barely good enough.

Revised Layer Summing 

Photoshop calculates the layers only in 8-bit integer space, this introduces inaccuracy to the layer summing (and to all layer operations). The below result is from revised summing: 

Picture 4: All the layers 1...8 active, revised summing

Starting arrangement for the layers:  

Layer 8	mode: normal, opacity: 50%
Layer 7	mode: normal, opacity: 100%
Layer 6	mode: normal, opacity: 50%
Layer 5	mode: normal, opacity: 100%
Layer 4	mode: normal, opacity: 50%
Layer 3	mode: normal, opacity: 100%
Layer 2	mode: normal, opacity: 50%
Layer 1	mode: normal, opacity: 100%

Now merge layers 1&2, 3&4, 5&6 and 7&8. With the resulting 4 layers do the same:
 

Layer 4'	mode: normal, opacity: 50%
Layer 3'	mode: normal, opacity: 100%
Layer 2'	mode: normal, opacity: 50%
Layer 1'	mode: normal, opacity: 100%

Now merge layers 1'&2', 3'&4'. With the resulting 2 layers do the same:
 

Layer 2''	mode: normal, opacity: 50%
Layer 1''	mode: normal, opacity: 100%

Finally merge layers 1''&2''. This will result much better summing than the original method.

If the eight 8-bit scans could be just summed to produce a higher bit-depth image the noise reduction would be optimal. A "Flatten to 16-bit" -operation would be rather useful.