# Noise spectrum

Discussion in 'Digital Photography' started by tsingh, Mar 8, 2005.

1. ### tsinghGuest

was concentrated in the higher frequencies. Is this true of
contemporary sensors?
Also, is the noise in a pixel (fairly) independent of the noise in
other pixels?

Now consider the following (brute force) scheme for producing low noise
images of a given resolution: oversample the image with a higher
resolution sensor, filter out the resulting higher frequencies and
scale down. If noise is independent across pixels, this should yield a
lower noise image than a lower resolution sensor would. How far can you
take this process, asymptotically?

As a concrete example, consider two 2 megapixel images - one from a 2M
sensor and another from a 4M sensor of the same size. Downsize the 4M
image to 2M using a decent algorithm like Lanczos. Which image will
have lower noise?

Thanks,
Tripurari

tsingh, Mar 8, 2005

2. ### Roger N. Clark (change username to rnclark)Guest

Unfortunately, you can't win this way. The reasons are:
the 2M sensor would have larger pixels, thus gather
more photons (in proportional to the area). The noise
from modern digital cameras is photon noise limited
at high signal levels and sensor read noise limited
at low levels. In your example, the signal-to-noise
of the 4M sensor would be half that of the 2M sensor
in each pixel. In that case, there is no theoretical
difference. But the read noise is relatively constant
for the two sensors (typical values are 10 to 20 electrons),
so the read noise is a higher proportion of the signal on
the 4M sensor, thus overall the 4M sensor with the smaller
pixels will be noisier, even if you averaged 2x2 pixels.

Examples with real digital cameras are shown at:
http://www.clarkvision.com/imagedetail/does.pixel.size.matter

Roger

Roger N. Clark (change username to rnclark), Mar 9, 2005

3. ### tsinghGuest

Ignore the read noise for the sake of argument.
If you average 2x2 pixels, you'd be comparing a 2M with an 8M image,
and not a 4M image. Let us stick with 8M as it is more convenient.

Sure, the 8M will be noisier, but what fraction of that noise will be
filtered out when downsizing? A good downsizing scheme will filter
differently than averaging 2x2 pixels. If noise is high-frequency
heavy, then the downsized image should be cleaner.

Regards,
Tripurari

tsingh, Mar 9, 2005
4. ### David J TaylorGuest

You need to factor in:

- the 8MP pixels will be smaller, and the readout circuitry may occupy a
greater fraction of the available area, making capture less efficient.

- how the eye responds to noise of different spatial frequencies at
different viewing distances.

- what the minimum resolveable contrast (or modulation) is for the eye at
a given spatial frequency.

I suspect that people who view prints close up may say: the 8MP is noiser,
but that people who view at "normal" viewing distances (arm's length for a
10 x 8 inch print) may say: the 8MP looks sharper. Between 2MP and
resampled 8MP - that would be good test to try!

David

David J Taylor, Mar 9, 2005
5. ### Bart van der WolfGuest

SNIP
That depends on the noise spectrum, but for argument sake let's assume
a White noise power spectrum.
I don't see why it should be high-frequency heavy, the Nyquist
frequency will still be the limit for the highest frequency. I made
the following empirical evaluation, using the Imatest program. A test
object (slanted edge for SFR/MTF measurement) without noise was
Gaussian blurred in Photoshop with 0.5 radius. That was to model a
resolution limited linear gamma image. I added a Uniform (white) noise
of 4%. That was down-sampled with ImageMagick's Sinc filtered resize
routine to 50% of each dimension.

This is the result for the three images:
<http://www.xs4all.nl/~bvdwolf/temp/Noise_before_and_after_Downsampling.png>
Image 1 at the top: Original resolution limited image has perfect S/N,
Image 2 in the middle: Noise added results in flat noise spectrum,
Image 3 at the bottom: Down sampled image still has a relatively flat
spectrum, although a bit high frequency attenuated due to
anti-aliasing Sinc prefilter, but the S/N is 2.4x as good which is
even better than the theoretical 2x for 4 samples due to change in
noise spectrum and MTF.

A better model would also include Poisson distributed Photon shot
noise, but it would make it more difficult to see the single effect of
downsampling because it varies with luminance as well.

Bart

Bart van der Wolf, Mar 9, 2005
6. ### Don Stauffer in MinneapolisGuest

There are LOTS of sources of noise. Many are independent of frequency.
In a scanned sensor the time spectrum has an effect. In a mosaiced
sensor, however, like a CCD, the temporal makeup of the noise is
unimportant. Each pixel is essentially a seperate sample. So in terms
of spatial frequency the noise content is indeed a high frequency
component. This is true for things like electronic noise.

If we consider things like flare and ghosts a 'noise', these will,
however, have lower spatial frequency values.

Don Stauffer in Minneapolis, Mar 9, 2005
7. ### tsinghGuest

With a white noise spectrum, there should be no difference between the
two cases.
I don't know why it should be, but I was under the impression that it
was. That was many years ago, I don't know if it is still true.
Thanks for the detailed study. The two cases should be identical.
Perhaps sharpening the down sampled image to compensate for he
pre-filter will also reduce the S/N down to 2.

This also raises a separate question - will the 8M down sampled image
have higher SNR than the 2M image because the camera's antialiasing
filter won't suppress the lower frequencies need to generate the 2M
image?
-Tripurari

tsingh, Mar 10, 2005
8. ### Ilya ZakharevichGuest

[A complimentary Cc of this posting was sent to

Probably you were looking for the noise in log-frequency scale; with
(creative) area-preserving log-scaling you may get an impression of
high-heavy.

E.g., there is 2x as much white noise power between 10KHz and 20KHz
than between 5KHz and 10KHz (taking aural analogy); but these
intervals are the same in log-scale.

Hope this helps,
Ilya

Ilya Zakharevich, Mar 10, 2005
9. ### Bart van der WolfGuest

In theory that might be the case, but the downsampling process makes
assumptions and suffers from limitations such as quantization errors
and non-infinite size. There are also things like the Gibbs phenomenon
(ringing) that will amplify and attenuate certain frequencies near the
Nyquist limit. That's why I determined the results empirically.

SNIP
Yes, it is common to sharpen after resampling in digital imaging, but
it will also increase the aliasing potential. That will manifest
itself as jagged lines and the finest noise will become more visible
because the aliases are imaged as larger noise structure. Therefore a
very small radius USM, e.g. amount 300 radius 0.3, and a threshold
suited for the image content is commonly applied, preferably with an
the photon signal, which is the only signal that's modified by the
optical AA-filter. That's what I also did with my test. The image was
pre-blurred first, the noise was then added.

However, there are also other considerations like dynamic range, that
will be worse for the smaller sensor elements. Also, smaller elements
require better lenses to deliver actual resolution. Down-sampling does
significantly improve the MTF of the image and the S/N ratio, but the
2MP image loses resolution versus the 8MP image for same size output,
because it requires more magnification.

In my example the resolution improved between 35-65% (depending on the
criterion), so magnifying that downsampled image by 2 again, would
reduce the resolution to less of what it was. If the final image needs
no magnification, then downsampling only brings quality benefits.

Bart

Bart van der Wolf, Mar 10, 2005
10. ### Don Stauffer in MinneapolisGuest

I think in these discussions, when we use the term spectrum, we need to
clarify whether we are talking spatial spectrum or temporal ones.
Ordinarily in speaking of electronic noise, we are referring to temperal
spectrum. However, when we view a still photograph, it is the spatial
spectrum, or spatial frequencies, we view.

In a scanning sensor, like a vidicon or mirror scanned IR sensors, there
IS a relationship between temporal and spatial spectra. In a mosaic
sensor, however, there is usually no relationship.

Don Stauffer in Minneapolis, Mar 10, 2005