Noise in photographic images

Introduction – Noise measurements – Noise appearance – Noise summary
Scene-reference noise, SNR, and Dynamic Range – Temporal noise – ISO 15739 noise and SNR
Noise spectrum – Links

Key noise-related web pages

Dynamic Range – a general introduction with links to Imatest modules that calculate it. Multicharts/Multitest/eSFR ISO Noise – including chroma, sensor (RAW), and visual noise Temporal Noise – comparing the two-image and multi-image measurements

Introduction

Noise is a random variation of image density, visible as grain in film and pixel level variations in digital images. It is a key image quality factor; nearly as important as sharpness. It is closely related to dynamic range— the range of brightness a camera can reproduce with reasonably good Signal-to-Noise Ratio (SNR) and contrast. Since it arises from basic physics— the photon nature of light and the thermal energy of heat— it will always be present. The good news is noise can be extremely low— often imperceptibly low— in digital cameras, particularly DSLRs with large pixels (4 microns square or larger). But noise can get ugly in compact digital cameras with tiny pixels, especially at high ISO speeds, and noise reduction software can have visible side-effects.

In most cases noise is perceived as a degradation in quality. But some Black & White photographers like its graphic effect: Many favored 35mm Tri-X film. (Film grain has very different statistics from digital noise— it’s multiplicative rather than additive, and its spectrum is dependent on density.) Pointillist painters, most notably George Seurat, created images from “noise” (specks of color) by hand; a task that can be accomplished in seconds today with Photoshop plugins. But by and large, the majority of photographers, especially color and large-format photographers, dislike noise with good reason. Noise is measured by several Imatest modules: Multicharts, Multitest, eSFR ISO, Colorcheck, Stepchart, and to a limited degree in SFR, SFRplus, and Uniformity. The first three modules— Multicharts, Multitest, and eSFR ISO— have the most comprehensive noise measurements.

Noise measurements typically refer to RMS (Root Mean Square) noise, which is identical to the standard deviation of the signal S.

RMS Noise = N =σ(S), where σ denotes the standard deviation.

S can be the signal in any one of several channels: R, G, B, Y (luminance, typically 0.2125 R + 0.7154 G + 0.0721 B), or a derived channel such as R-Y or B-Y (both used for chroma noise). L*, a*, b*, or others. See Multicharts/Multitest/eSFR ISO noise measurements.

Correcting noise in patches with nonuniform illumination Imatest calculations may deviate slightly from the N =σ(S) formulation because the patch used to measure noise may be unevenly illuminated, and this can result in an increase in measured N not actually caused by random noise itself. To account for this we calculate second order fits to the mean signal value in both the x and y-directions, then subtract the second order fits from the signal prior to calculating noise. Hence Imatest noise measurements may be slightly lower than plain standard deviations. The Imatest calculation can be set in a dropdown menu in the settings windows for modules that calculate noise. We recommend New noise uniformity corr. (BEST), but there is an option (not recommended) for turning the nonuniformity correction off. The old calculation has been removed.

 

Signal-to-Noise Ratio (SNR) is a measurement derived from noise that is often considered more important than noise itself. It is expressed as either a simple ratio (SNR = S/N) or in decibels, SNR(dB) = 20 log₁₀(S/N), familiar to electrical engineers. In digital cameras noise consists of two parts: fixed noise (sensor dark current noise and thermal (resistive) noise) and shot (photon) noise, which increases with the square root of the mean number of photons striking the pixels.

Noise measurements

Noise measurements should ideally

• correlate with perceived appearance,
• (in many cases) be referenced to the original scene so the measurement is not affected by the tonal response (gamma, equivalent to contrast) of the camera or RAW converter,
• be detailed enough to allow accurate assessment of sensor and camera performance, and
• be simple enough to interpret without difficulty.

SNR— Since noise is only meaningful in relationship to a signal, a Signal-to Noise Ratio (SNR or S/N) is often calculated. SNR can be defined in many ways, depending on how Signal S is defined. For example, S can be an individual patch pixel level or the pixel difference corresponding to a specified scene density range (1.45 or 1.5 are often used for this purpose) or a low contrast object (for Contrast Resolution SNR). It is important to know precisely how SNR is defined whenever it is discussed. SNR can be expressed as a simple ratio (S/N) or in decibels (dB), where SNR (dB) = 20 log₁₀(S/N). Doubling S/N corresponds to increasing SNR (dB) by 6.02 dB. Since these requirements can be somewhat contradictory, Imatest modules have several noise and SNR measurements, some simple and some detailed.

Multicharts, Multitest, Stepchart, and Colorcheck include the following noise displays:

• Noise a function of pixel level or exposure, expressed in
  • Pixels, normalized to the pixel difference corresponding to a scene density range of 1.5 for Stepchart (comparable to the density range of 1.45 for the GretagMacbeth ColorChecker) or the White – Black zones in the ColorChecker (row 3, patches 1 – 6; density range = 1.45). Without this normalization, noise is a function of RAW converter response curve; it increases with converter contrast.
  • Pixels, normalized to the maximum pixel value: 255 for 8/24-bit files.
  • Pixels (maximum of 255 for 8/24-bit files)
  • f-stops (or EV or zones; a factor of two in exposure), i.e., referenced to the original scene. Noise measured in f-stops corresponds closely to human vision. See f-stop noise, below.
• Noise as a simple (average) number
  • A good single number for describing noise is the average noise of the Y (Luminance) channel, measured in pixels (normalized scene density difference of 1.5), shown in the lower plot in the figures, below. The lightest and darkest zones, representing chart densities greater than 1.5 or less than 0.1 are excluded from the average.
• S/N or SNR (dB) as a function of pixel level or exposure, where S is the pixel level of the individual test chart patch.
• S/N or SNR (dB) as a simple (average) number.
  • A good single number for defining SNR is the White – Black SNR, SNR_BW, where S is the difference in pixel levels between the White and Black patches in the GretagMacbeth ColorChecker in Colorcheck (density range of 1.45), or the pixel difference corresponding to a chart (scene) density difference of 1.5 in Stepchart. Noise N is measured in a gray patch with density around 0.7. SNR_BW was developed to reduce the effect of image contrast (resulting from image processing, i.e., the application of a gamma curve) on the noise measurements.
    \( SNR_{BW} = 20 log_{10}bigl( frac{S_{WHITE} – S_{BLACK}}{N_{MID}} bigr) \)
• a noise spectrum plot, described below.

Uniformity displays a spatial map of noise.

Multicharts, Multitest, and eSFR ISO contain the most comprehensive noise analysis and displays. The various noise calculations (which include everything from Stepchart and Colorcheck) are listed in the following table (more are added from time to time).

1.	Noise vs. input density (RGB) Noise in pixels or % of maximum pixel level	2.	Simple noise or SNR derived from standard deviation (σ) of pixel levels.
2.	Signal/Noise (S/N) vs. input density (RGBY) The luminance (Y-channel) is used for S.
3.	SNR (dB) vs. input density (RGBY) SNR (dB) = 20 log10(S/N).
4.	Chroma noise vs. input density	3.	Industry-standard chroma noise
5.	Chroma S/N vs. input density
6.	Chroma SNR (dB) vs. input density
7.	CIELAB (L*a*b*) noise	3.	Experimental: Seems to make sense since CIELAB is approximately perceptually uniform, but has no industry traction.
8.	CIELAB (L*a*b*) S/N
9.	CIELAB (L*a*b*) SNR (dB)
10.	Noise vs. pixel (all patches)	2.	For characterizing sensors from RAW (unprocessed or minimally processed) images.
11.	S/N vs. pixel (all patches)
12.	SNR (dB) vs. pixel (all patches)
13.	F-stop (scene-referenced) noise, including Dynamic Range results.	2.	Used for Dynamic Range calculations. Defined here.
14.	Scene-referenced S/N (ratio), including Dynamic Range results.
15.	Scene-referenced SNR (dB), including Dynamic Range results.
16.	ISO 15739 Visual noise vs. input density (L*u*v*)	V.	From the ISO 15739:2013 standard. Includes viewing conditions.
17.	ISO 15739 Visual S/N vs. input density (L*u*v*)
18.	ISO 15739 Visual SNR (dB) vs. input density (L*u*v*)
19.	ISO 15739 Noise and Dynamic Range	2.	Also from ISO 15739:2013. Completely independent of visual noise.
20.	ISO 15739 Signal/Noise (S/N) and Dynamic Range
21.	ISO 15739 Signal-to-Noise Ratio (SNR) in dB
22.	CPIQ Visual Noise (CIELAB)	V.
23.	CPIQ Visual S/N (CIELAB)
24.	CPIQ Visual SNR (dB) (CIELAB)
25.	YUV noise	3.
26.	YUV S/N
27.	YUV SNR (dB)

The entry in the third column is from the Noise settings window: 1. No noise, 2. Elementary noise (fast calculations), 
3. Advanced noise (slower), and V. Visual noise (separate settings for ISO and CPIQ visual noise).

Noise appearance The appearance of noise is illustrated in the stepchart images on the right. Noise is usually measured as an RMS (root mean square) voltage. The mathematics of noise is presented in a green box at the bottom of this page. The stepcharts in columns (A)-(C) are simulated. They are assumed to have a minimum density of 0.05 and density steps of 0.1, identical to the Kodak Q-13 and Q-14. They have been encoded with gamma = 1/2.2 for optimum viewing at gamma = 2.2 (the Windows/Internet standard). Strong noise— more than you’d find in most digital cameras— has been added to columns (A) and (B). Column (C) is noiseless. The fourth column (D) contains an actual Q-13 stepchart image taken with the Canon EOS-10D at ISO 1600: a very ISO high speed. Noise is visible, but low for such a high ISO speed (thanks, no doubt, to software noise reduction). The noise in (A) is constant inside the sensor, i.e., before gamma encoding. When it is encoded with gamma = 1/2.2, contrast, and hence noise, is boosted in dark areas and reduced in light areas. The On Semiconductor publication, CCD Image Sensor Noise Sources, indicates that this is not a realistic case. Sensor noise tends to increase with brightness. The noise in (B) is uniform in the image file, i.e., its value measured in pixels is constant. This noise must therefore increase with brightness inside the sensor (prior to gamma encoding), and hence is closer to real sensor behaviour than (A). Noise appears relatively constant except for the darkest zones, where it’s not clearly visible. Noise is often lower in the lightest zones, where a tonal response “S” curve superimposed on the gamma curve (or saturation) reduces contrast, hence noise. For this reason the middle zones— where noise is most visible— are used to calculate the average noise: a single number used to characterize overall noise performance. We omit zones where the density of the original chart (hence display density in an unmanipulated image) is greater than 1.5 or less than 0.1. Characteristic Stepchart results are shown below.

(A) Const. sensor noise (B) Const. pixel noise (C) No noise (D) Canon EOS-10D ISO 1600

 

Column (B): Uniform pixel noise This image has simulated uniform pixel noise (i.e., constant noise in the image file, measured in pixels). The upper plot is the tonal response (or characteristic curve) of the camera. It shows the expected ideal response for encoding with gamma = 1/2.2 = 0.4545: a straight line with slope = 0.4545 for the log-log plot. The middle plot shows noise measured in f-stops (or EV or zones). Noise increases more steeply for dark regions (large negative values of Log Exposure) in actual sensors. The lower plot shows noise measured in pixel levels, normalized to the difference in pixel levels for a density range of 1.5. It is relatively constant, showing only statistical variation, except for the brightest level (on the right), where the noise is reduced because some samples are clipped at pixel level 255. The lower plot also contains the single number used to characterize overall noise performance: the average Luminance channel noise (Y = 5.59%, on the right near the top). This number is very high; it corresponds to poor image quality. This is SNR in dB for simulated uniform pixel noise. Because of the gamma = 2.2 encoding, SNR inproves by 6.02/2.2 = 2.74 dB for each doubling of exposure (0.301 density units); roughly 9.1 dB per decade (1 density unit).

Column (D): Canon EOS-10D at ISO 1600 Unlike the above figure (for the image in column (B)), real data for the Canon EOS-10D at ISO 1600 is used.The upper plot shows a slight tonal response “S” curve superimposed on the gamma curve (which is a straight line in this log-log plot). Some converter settings (such as “low contrast”) result in a much more pronounced “S” curve. The middle plot shows f-stop noise, which increases dramatically in the dark regions. The lower plot shows the normalized pixel noise. It increases in the dark regions. This increase is due in part to the high ISO speed. Digital cameras achieve high ISO speed by amplifying the sensor output, which boosts noise, particularly in dark regions. This curve looks different for the minimum ISO speed: noise values are much lower and subject to more statistical variation. This is SNR in dB for the Canon EOS-10D at ISO 1600. (This display option was introduced with Imatest 2.3.16). SNR improves by about 6 dB for each doubling of exposure (0.301 density units); roughly 20 dB per decade (1 density unit), which is what would be expected for constant sensor noise. (This curve would be dramatically different at lower ISO speeds.)

Noise summary

There are two basic types of noise.

• Temporal. Noise which varies randomly each time an image is captured. Measured by  Multicharts, Multitest, Colorcheck, and Stepchart using two identical input images for all modules or multiple images (4-16 with 8 recommended) for Multicharts and Multitest, as described in Measuring Temporal Noise.
• Spatial or fixed pattern. Noise caused by sensor nonuniformities. Sensor designers have greatly reduced fixed pattern noise in the last decade.

Temporal noise can be reduced by signal averaging, which involves summing N images, then dividing by N. This is an option for all Imatest analysis modules when several image files are selected (you can also analyze the individual files separately). Summing N individual images increases the summed signal pixel level (voltage) by N. But since temporal noise is uncorrelated, noise power (rather than voltage or pixel level) is summed. Since voltage is proportional to \(sqrt{text{power}}\), the noise pixel level (which is proportional to noise voltage) increases by \(sqrt{N}\). Signal-to-noise ratio (S/N or SNR) improves by \(N / sqrt{N} = sqrt{N}\). S/N is improved by a factor of 2 (6.01 dB) for 4 images, 4 for 16 images, etc.

Several factors affect noise.

• Pixel size. Simply put, the larger the pixel, the more photons reach it, and hence the better the signal-to-noise ratio (SNR) for a given exposure. The number of electrons generated by the photons is proportional to the sensor area (as well as the quantum efficiency). Noise power is also proportional to the sensor area, but noise voltage is proportional to the square root of power and hence area. If you double the linear dimensions of a pixel, you double the SNR. The electron capacity of a pixel is also proportional to its area. This directly affects dynamic range.
• Sensor technology and manufacturing. The biggest technology issue is CMOS vs. CCD. We won’t discuss it in detail here. Until 2000 CMOS was regarded as having worse noise, but it has improved to the point where the two technologies are comparable, differing only in detail. CMOS is less expensive because it is easy to add functionality to the sensor chip. Technology also involves other aspects of sensor design and manufacturing, all of which will improve gradually with time.
• ISO speed (Exposure Index) setting. Digital cameras control ISO speed by amplifying the signal (along with the noise) at the pixel. Hence, the higher the ISO speed the worse the noise. To fully characterize a sensor it must be tested at several ISO speeds, including the lowest and highest.
• Exposure time. Long exposures with dim light tend to be noisier than short exposures with bright light, i.e., reciprocity doesn’t work perfectly for noise. To fully characterize a sensor it should be tested at long exposure times (several seconds, at least).
• Digital processing. Sensors typically have 12-bit analog-to-digital (A-to-D) converters, so digitization noise isn’t usually an issue at the sensor level. But when an image is converted to an 8-bit (24-bit color) JPEG, noise increases slightly. The noise increase can be worse (“banding” can appear) if extensive image manipulation (dodging and burning) is required. Hence it is often best to convert to 16-bit (48-bit color) files. But the output file bit depth makes little difference in the measured noise of (unmanipulated) files.
• Raw conversion. Raw converters often apply noise reduction (lowpass filtering) and sharpening (see Noise frequency spectrum, below), whether you want it or not; even if NR and sharpening are turned off. This makes it difficult to measure the sensor’s intrinsic properties.

General comments

• Imatest subtracts gradual pixel level variations from the image before calculating noise (the standard deviation of pixel levels in the region under test). This removes errors that could be caused by uneven lighting. Nevertheless, you should take care to illuminate the target as evenly as possible.
• The target used for noise measurements should be smooth and uniform– grain (in film targets) or surface roughness (in reflective targets) should not be mistaken for sensor noise. Appropriate lighting (using more than one lamp) can minimize the effects of surface roughness.