Image registration/averaging and image quality

1) In the ideal case the registration and averaging of, for instance
150 individual 8bit noisy images will improve SNR by log10(n x 256),
and the dynamic range from ~2.4 to ~4.6. However, when aligning low SNR
images, the match is not always perfect (or rather, it is almost never
perfect). Under such circumstances how does one model the change in
SNR.

2) Is there a better metric to characterize the improvement in
resolving power, or resolution, when registering and averaging multiple
frames

Thanks!

Piotr wrote:
> 1) In the ideal case the registration and averaging of, for instance
> 150 individual 8bit noisy images will improve SNR by log10(n x 256),
> and the dynamic range from ~2.4 to ~4.6. However, when aligning low SNR
> images, the match is not always perfect (or rather, it is almost never
> perfect). Under such circumstances how does one model the change in
> SNR.
>
> 2) Is there a better metric to characterize the improvement in
> resolving power, or resolution, when registering and averaging multiple
> frames

You may want to ask such questions in the sci.image.processing
usenet group.

Rune

Piotr wrote:
> 1) In the ideal case the registration and averaging of, for instance
> 150 individual 8bit noisy images will improve SNR by log10(n x 256),

Where does that come from? for one dimension and white Gaussian noise, 
the improvement is not log10(256*n), but sqrt(n). That yields 
improvement by factor of 16, or 12 dB.

> and the dynamic range from ~2.4 to ~4.6. However, when aligning low SNR
> images, the match is not always perfect (or rather, it is almost never
> perfect). Under such circumstances how does one model the change in
> SNR.
> 
> 2) Is there a better metric to characterize the improvement in
> resolving power, or resolution, when registering and averaging multiple
> frames

Noise and resolution are not exactly related. Under some unlikely 
circumstances, you could gain 4 bits of resolution.

If your 8-bit converter had the linearity of a 12-bit, and the noise 
happened to simulate a nearly ideal dithering waveform, and signal were 
stationary during the averaging process, then the average of 256 
conversions would be accurate to 12 bits. How that affects the 
resolution of an image would be better answered in another group.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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Hi Jerry-

Thanks for reply!

>> 1) In the ideal case the registration and averaging of, for instance
>> 150 individual 8bit noisy images will improve SNR by log10(n x 256),

> Where does that come from? for one dimension and white Gaussian noise,
> the improvement is not log10(256*n), but sqrt(n). That yields
> improvement by factor of 16, or 12 dB.

>> and the dynamic range from ~2.4 to ~4.6. However, when aligning low SNR
>> images, the match is not always perfect (or rather, it is almost never
>> perfect). Under such circumstances how does one model the change in
>> SNR.

Sorry, there was a mixup - it's the dynamic range that is derived from
log10(n x 256) 
(we're having a heat-wave in the UK at the moment)...