digital image noise

Introduction:

digital sensors produce artefacts called digital noise
each camera type has different noise characteristics at different ISO's, operating temperature and exposure
in normal photography (meaning bright light photography), noise is usually a secondary consideration, since the signal component easily overwhelms it.
- astrophotography differs from normal photography by being signal limited - in almost all cases the bottleneck is the available light input. Usually, the signal is of only slightly greater amplitude than the noise (thermal charge carriers, Johnson noise, schot noise, readout noise, bias noise for any EEs that may be reading this). This is the dominating differential of astrophotography from normal photography.
sensitivity in a detector is composed of two components:
- responsivity is the detector output in response to the incident signal.
- noise is the same detector's response to all other parameters.
sensitivity is a function of the ratio of Signal to Noise. A detector that produces a huge output in response to a small input is not sensitive if it also produces a huge noise component.
image noise is caused by several factors, producing different contributions to the noise:
- photon counting statistics noise:
  - even if a sensor could convert each photon hitting it into an electron which could then be counted without added noise, there will still be noise due to the statistics of counting photons which is equal to the square root of the number of photons.
  - SNR due to photon counting noise then = no. photons (the signal) / square root of no. of photons (noise)
  - thus SNR due to photon counting noise = square root of no. of photons
  - this noise is what dominates the noise in modern digital camera sensors
  - the sensor stores the electrons until they are transferred from the sensor chip to the camera electronics, and each sensor has a capacity for storing such electrons called the Full Well Capacity. The greater this capacity, the greater the SNR according to the above equation. This capacity is generally proportional to the pixel pitch in microns.
  - examples of approximate Full Well Capacities (from R.Clark):
    - S/N 90-100: Canon 5D / 1DMII = 80,000 electrons; Canon 20D/NikonD70 = 50,000 electrons;
    - S/N 70-80: Nikon D200 / D50 = 30,000-33,000 electrons;
    - S/N 40-50: Canon S60 = 22,000 electrons;
    - S/N 25-30: Canon S70 = 9,000 electrons;
- read noise:
  - this is the noise floor for low signal detection
  - it is possible to see a image of the signal if the signal is at least 1/10th the read noise.
  - modern Canon sensors have read noise of 3-4 electrons, while sensors in Nikon dSLRs tend to have read noise of 6-8 electrons.
- thermal noise:
  - becomes prominent with long exposures, especially at higher sensor temperatures.
  - characteristically is quite variable from pixel to pixel.
  - can be subtracted out by taking a “dark frame” (eg. with the lens cap on for the same exposure).
- amp noise:
  - Amplifier glow is not caused by heat leaking from the on-chip CCD amplifier. Unlike thermal noise, you cannot control it by cooling the CCD. You can control it by turning off the amplifier during exposure. Webcams have been hacked to do this. Some modern Canon dSLRs have been programmed to do this for long exposures.
  - The light originates from the electrons moving through the amplifier transistors (MOSFETs). Light can be emitted by hot majority charge carriers (e.g., electrons) moving between the source and drain in a MOSFET. A blackbody spectrum is associated with these hot carriers. Thermally generated (blackbody) photons with wavelengths above the band gap are re-absorbed in the silicon and those with wavelengths greater than ~1100 nm escape the silicon. Photon counting detectors sensitive at near IR wavelengths beyond 1100 nm are used as sensors in diagnostics for CMOS circuits. IBM and others have used this diagnostic. This is the true source of “amplifier glow”.
  - for more info:
    - http://www.credence.com/emiscope_tutorial/tut_dynamic_emission.html
    - http://www.stsci.edu/hst/nicmos/performance/anomalies/ampglow.html

Noise reduction:

physical techniques:
- cooling the sensor
- minimising sensor over-heating by limiting use of Live Preview, etc.
in-camera processing:
- automatic dark frame subtraction to reduce thermal noise in long exposures
- choice of ISO setting - the lower the ISO, the lower the image noise
- in-camera noise processing
  - some Nikon dSLR's apply noise reduction even to RAW files hence the need for “mode 3” to disable this for astrophotography.
  - most other manufacturers only apply NR to jpegs and not to the RAW files.
  - most cameras give you an option of turning it on or off and in some cases how aggressive it should be (eg. Olympus E510)
post-processing:
- manual dark frame subtraction to reduce thermal noise in long exposures
- manual bias frames
- image stacking:
  - taking multiple sub-exposures of stationary faint subjects such as nebulae then using software to combine them.
  - improves:
    - signal:noise ratio
      - stacking reduces the impact of random noise (not constant thermal noise - this is reduced by subtracting dark frames)
    - dynamic range
      - stacking increases the number of possible digitized values linearly with the number of images stacked.
      - stacking thus allows you to increase the brightness of dim pixels to above the range of noise
- noise reduction software techniques:
  - denoising involves a compromise between reducing image noise and retaining detail and texture.
  - use of Gaussian blur to minimise appearance of residual noise
  - wavelet-based noise reduction:
    - NeatImage
    - Imagenomic
  - bilateral filtering
  - anisotropic diffusion
  - PDE-based methods
  - fields of experts
  - nonlocal methods
  - multiple image deblurring and denoising:
    - http://research.microsoft.com/users/jiansun/papers/Deblurring_SIGGRAPH07.pdf
      - utilises the sharp image structures in the noisy image to estimate a kernel of the blurred image, then applies residual deconvolution and gain-controlled deconvolution