Sum Noise Notes

There's a large amount of discussion about the best way to combine sets of images. These notes compare "summing" images vs. "averaging" images.

Intuitively, one is tempted to dismiss the differences. After all, we learned in grade school that an arithmetic average is just the sum of a group of values divided by the number of values. So there should be no difference between the sum and an average except for an integer scale factor.

However, in the real world, differences can arise that contribute significantly to the quality of the resultant, processed images depending on the software and methods used.

What follows is a dramatic example using a real image, artificially corrupted by noise.

Original HST image, copied from the web  
The original image with Gaussian noise of amplitude 20 added using MaxIm DL.

This image was then scaled down by a factor of 32 to simulate a low contrast image corrupted by noise.

The eye is very good at averaging noise spatially, so even though just 8 gray levels remain, the image will appear pretty good.

 
The above process was repeated 32 times, simulating taking 32 images under ideal seeing conditions, only corrupted by noise.

The image to the left is an arithmetic average of these 32 frames. The average was then saved as a normal integer TIFF file.

This image was then re-loaded and scaled to show the quantization effects (also called posterization)

The same data set but averaged using floating point values, then stretched to a full 8-bits THEN saved as an integer file.

The same data set was stacked using median processing. Note that since the original data were quantized, the median is as well. The median function will not add intermediate gray values like a floating point average or sum will.

Alternatively, one can scale the image PRIOR to averaging. This too allows the integer arithmetic to extract more gray levels through the image average.

This image is the result of summing the 32 frames then scaling the resultant image and saving the result.  
That summed image was then unsharp masked to bring out further detail. No effort was made to optimize the settings, the processing was simply done to show that one can usefully process the resultant summed image.