Image noise

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Noise clearly visible in an image from a digital camera Highimgnoise.jpg
Noise clearly visible in an image from a digital camera

Image noise is random variation of brightness or color information in images, and is usually an aspect of electronic noise. It can be produced by the image sensor and circuitry of a scanner or digital camera. Image noise can also originate in film grain and in the unavoidable shot noise of an ideal photon detector. Image noise is an undesirable by-product of image capture that obscures the desired information.

Contents

The original meaning of "noise" was "unwanted signal"; unwanted electrical fluctuations in signals received by AM radios caused audible acoustic noise ("static"). By analogy, unwanted electrical fluctuations are also called "noise". [1] [2]

Image noise can range from almost imperceptible specks on a digital photograph taken in good light, to optical and radioastronomical images that are almost entirely noise, from which a small amount of information can be derived by sophisticated processing. Such a noise level would be unacceptable in a photograph since it would be impossible even to determine the subject.

Types

Gaussian noise

Principal sources of Gaussian noise in digital images arise during acquisition. The sensor has inherent noise due to the level of illumination and its own temperature, and the electronic circuits connected to the sensor inject their own share of electronic circuit noise. [3]

A typical model of image noise is Gaussian, additive, independent at each pixel, and independent of the signal intensity, caused primarily by Johnson–Nyquist noise (thermal noise), including that which comes from the reset noise of capacitors ("kTC noise"). [4] Amplifier noise is a major part of the "read noise" of an image sensor, that is, of the constant noise level in dark areas of the image. [5] In color cameras where more amplification is used in the blue color channel than in the green or red channel, there can be more noise in the blue channel. [6] At higher exposures, however, image sensor noise is dominated by shot noise, which is not Gaussian and not independent of signal intensity. Also, there are many Gaussian denoising algorithms. [7]

Salt-and-pepper noise

Image with salt and pepper noise Noise salt and pepper.png
Image with salt and pepper noise

Fat-tail distributed or "impulsive" noise is sometimes called salt-and-pepper noise or spike noise. [8] An image containing salt-and-pepper noise will have dark pixels in bright regions and bright pixels in dark regions. [9] This type of noise can be caused by analog-to-digital converter errors, bit errors in transmission, etc. [10] [11] It can be mostly eliminated by using dark frame subtraction, median filtering, combined median and mean filtering [12] and interpolating around dark/bright pixels.

Dead pixels in an LCD monitor produce a similar, but non-random, display. [13]

Shot noise

The dominant noise in the brighter parts of an image from an image sensor is typically that caused by statistical quantum fluctuations, that is, variation in the number of photons sensed at a given exposure level. This noise is known as photon shot noise. [6] Shot noise has a root-mean-square value proportional to the square root of the image intensity, and the noises at different pixels are independent of one another. Shot noise follows a Poisson distribution, which except at very high intensity levels approximates a Gaussian distribution.

In addition to photon shot noise, there can be additional shot noise from the dark leakage current in the image sensor; this noise is sometimes known as "dark shot noise" [6] or "dark-current shot noise". [14] Dark current is greatest at "hot pixels" within the image sensor. The variable dark charge of normal and hot pixels can be subtracted off (using "dark frame subtraction"), leaving only the shot noise, or random component, of the leakage. [15] [16] If dark-frame subtraction is not done, or if the exposure time is long enough that the hot pixel charge exceeds the linear charge capacity, the noise will be more than just shot noise, and hot pixels appear as salt-and-pepper noise.

Quantization noise (uniform noise)

The noise caused by quantizing the pixels of a sensed image to a number of discrete levels is known as quantization noise. It has an approximately uniform distribution. Though it can be signal dependent, it will be signal independent if other noise sources are big enough to cause dithering, or if dithering is explicitly applied. [11]

Film grain

The grain of photographic film is a signal-dependent noise, with similar statistical distribution to shot noise. [17] If film grains are uniformly distributed (equal number per area), and if each grain has an equal and independent probability of developing to a dark silver grain after absorbing photons, then the number of such dark grains in an area will be random with a binomial distribution. In areas where the probability is low, this distribution will be close to the classic Poisson distribution of shot noise. A simple Gaussian distribution is often used as an adequately accurate model. [11]

Film grain is usually regarded as a nearly isotropic (non-oriented) noise source. Its effect is made worse by the distribution of silver halide grains in the film also being random. [18]

Anisotropic noise

Some noise sources show up with a significant orientation in images. For example, image sensors are sometimes subject to row noise or column noise. [19]

Periodic noise

A common source of periodic noise in an image is from electrical or electromechanical interference during the image capturing process. [8] An image affected by periodic noise will look like a repeating pattern has been added on top of the original image. In the frequency domain this type of noise can be seen as discrete spikes. Significant reduction of this noise can be achieved by applying notch filters in the frequency domain. [8] The following images illustrate an image affected by periodic noise, and the result of reducing the noise using frequency domain filtering. Note that the filtered image still has some noise on the borders. Further filtering could reduce this border noise, however it may also reduce some of the fine details in the image. The trade-off between noise reduction and preserving fine details is application specific. For example if the fine details on the castle are not considered important, low pass filtering could be an appropriate option. If the fine details of the castle are considered important, a viable solution may be to crop off the border of the image entirely.

An image injected with periodic noise Noisy Smithsonian Castle.jpg
An image injected with periodic noise
Application of frequency domain notch filters Filtered Smithsonian Castle.jpg
Application of frequency domain notch filters

In digital cameras

Image on the left has exposure time of >10 seconds in low light. The image on the right has adequate lighting and 0.1 second exposure. Noise Comparison.JPG
Image on the left has exposure time of >10 seconds in low light. The image on the right has adequate lighting and 0.1 second exposure.

In low light, correct exposure requires the use of slow shutter speed (i.e. long exposure time) or an opened aperture (lower f-number), or both, to increase the amount of light (photons) captured which in turn reduces the impact of shot noise . If the limits of shutter (motion) and aperture (depth of field) have been reached and the resulting image is still not bright enough, then higher gain (ISO sensitivity) should be used to reduce read noise. On most cameras, slower shutter speeds lead to increased salt-and-pepper noise due to photodiode leakage currents. At the cost of a doubling of read noise variance (41% increase in read noise standard deviation), this salt-and-pepper noise can be mostly eliminated by dark frame subtraction. Banding noise, similar to shadow noise, can be introduced through brightening shadows or through color-balance processing. [20]

Read noise

In digital camera photography, the incoming photons (light) are converted to a voltage. This voltage then passes through the signal processing chain of the digital camera and is digitized by an analog to digital converter. Any voltage fluctuations in the signal processing chain, that contribute to a deviation of analog to digital units, from the ideal value proportional to the photon count, is called read noise. [21]

Effects of sensor size

The size of the image sensor, or effective light collection area per pixel sensor, is the largest determinant of signal levels that determine signal-to-noise ratio and hence apparent noise levels, assuming the aperture area is proportional to sensor area, or that the f-number or focal-plane illuminance is held constant. That is, for a constant f-number, the sensitivity of an imager scales roughly with the sensor area, so larger sensors typically create lower noise images than smaller sensors. In the case of images bright enough to be in the shot noise limited regime, when the image is scaled to the same size on screen, or printed at the same size, the pixel count makes little difference to perceptible noise levels – the noise depends primarily on sensor area, not how this area is divided into pixels. For images at lower signal levels (higher ISO settings), where read noise (noise floor) is significant, more pixels within a given sensor area will make the image noisier if the per pixel read noise is the same.

For example, the noise level produced by a Four Thirds sensor at ISO 800 is roughly equivalent to that produced by a full frame sensor (with roughly four times the area) at ISO 3200, and that produced by a 1/2.5" compact camera sensor (with roughly 1/16 the area) at ISO 100. This ability to produce acceptable images at higher sensitivities is a major factor driving the adoption of DSLR cameras, which tend to use larger sensors than compacts. An example shows a DSLR sensor at ISO 400 creating less noise than a point-and-shoot sensor at ISO 100. [22]

Sensor fill factor

The image sensor has individual photosites to collect light from a given area. Not all areas of the sensor are used to collect light, due to other circuitry. A higher fill factor of a sensor causes more light to be collected, allowing for better ISO performance based on sensor size. [23]

Sensor heat

Temperature can also have an effect on the amount of noise produced by an image sensor due to leakage. With this in mind, it is known that DSLRs will produce more noise during summer than in winter. [15]

Noise reduction

An image is a picture, photograph or any other form of 2D representation of any scene. [24] Most algorithms for converting image sensor data to an image, whether in-camera or on a computer, involve some form of noise reduction. [25] [26] There are many procedures for this, but all attempt to determine whether the actual differences in pixel values constitute noise or real photographic detail, and average out the former while attempting to preserve the latter. However, no algorithm can make this judgment perfectly (for all cases), so there is often a tradeoff made between noise removal and preservation of fine, low-contrast detail that may have characteristics similar to noise.

A simplified example of the impossibility of unambiguous noise reduction: an area of uniform red in an image might have a very small black part. If this is a single pixel, it is likely (but not certain) to be spurious and noise; if it covers a few pixels in an absolutely regular shape, it may be a defect in a group of pixels in the image-taking sensor (spurious and unwanted, but not strictly noise); if it is irregular, it may be more likely to be a true feature of the image. But a definitive answer is not available.

This decision can be assisted by knowing the characteristics of the source image and of human vision. Most noise reduction algorithms perform much more aggressive chroma noise reduction, since there is little important fine chroma detail that one risks losing. Furthermore, many people find luminance noise less objectionable to the eye, since its textured appearance mimics the appearance of film grain.

The high sensitivity image quality of a given camera (or RAW development workflow) may depend greatly on the quality of the algorithm used for noise reduction. Since noise levels increase as ISO sensitivity is increased, most camera manufacturers increase the noise reduction aggressiveness automatically at higher sensitivities. This leads to a breakdown of image quality at higher sensitivities in two ways: noise levels increase and fine detail is smoothed out by the more aggressive noise reduction.

In cases of extreme noise, such as astronomical images of very distant objects, it is not so much a matter of noise reduction as of extracting a little information buried in a lot of noise; techniques are different, seeking small regularities in massively random data.

Video noise

In video and television, noise refers to the random dot pattern that is superimposed on the picture as a result of electronic noise, the 'snow' that is seen with poor (analog) television reception or on VHS tapes. Interference and static are other forms of noise, in the sense that they are unwanted, though not random, which can affect radio and television signals.

Digital video noise is sometimes present on videos encoded in MPEG-2 format as a compression artifact

Useful noise

High levels of noise are almost always undesirable, but there are cases when a certain amount of noise is useful, for example to prevent discretization artifacts (color banding or posterization). Some noise also increases acutance (apparent sharpness). Noise purposely added for such purposes is called dither; it improves the image perceptually, though it degrades the signal-to-noise ratio.

Low and high-ISO noise examples

Low and high-ISO technical examination

Photon noise simulation. Number of photons per pixel increases from left to right and from upper row to bottom row. Photon-noise.jpg
Photon noise simulation. Number of photons per pixel increases from left to right and from upper row to bottom row.

An image sensor in a digital camera contains a fixed amount of pixels (which define the advertised megapixels of the camera). These pixels have what is called a well depth. [27] The pixel well can be thought of as a bucket. [28]

The ISO setting on a digital camera is the first (and sometimes only) user adjustable (analog) gain setting in the signal processing chain. It determines the amount of gain applied to the voltage output from the image sensor and has a direct effect on read noise. All signal processing units within a digital camera system have a noise floor. The difference between the signal level and the noise floor is call the signal-to-noise ratio. A higher signal-to-noise ratio equates to a better quality image. [29]

In bright sunny conditions, a slow shutter speed, wide open aperture, or some combination of all three, there can be sufficient photons hitting the image sensor to completely fill, or otherwise reach near capacity of the pixel wells. If the capacity of the pixel wells is exceeded, this equates to over exposure. When the pixel wells are at near capacity, the photons themselves that have been exposed to the image sensor, generate enough energy to excite the emission of electrons in the image sensor and generate sufficient voltage at the image sensor output, [21] equating to a lack of need for ISO gain (higher ISO above the base setting of the camera). This equates to a sufficient signal level (from the image sensor) which is passed through the remaining signal processing electronics, resulting in a high signal-to-noise ratio, or low noise, or optimal exposure.

Conversely, in darker conditions, faster shutter speeds, closed apertures, or some combination of all three, there can be a lack of sufficient photons hitting the image sensor to generate a suitable voltage from the image sensor to overcome the noise floor of the signal chain, resulting in a low signal-to-noise ratio, or high noise (predominately read noise). In these conditions, increasing ISO gain (higher ISO setting) will increase the image quality of the output image, [30] as the ISO gain will amplify the low voltage from the image sensor and generate a higher signal-to-noise ratio through the remaining signal processing electronics.

It can be seen that a higher ISO setting (applied correctly) does not, in and of itself, generate a higher noise level, and conversely, a higher ISO setting reduces read noise. The increase in noise often found when using a higher ISO setting is a result of the amplification of shot noise and a lower dynamic range as a result of technical limitations in current technology.

See also

Related Research Articles

Charge-coupled device Device for the movement of electrical charge

A charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a major technology used in digital imaging.

Photodiode Converts light into current

A photodiode is a semiconductor p-n junction device that converts light into an electrical current. The current is generated when photons are absorbed in the photodiode. Photodiodes may contain optical filters, built-in lenses, and may have large or small surface areas. Photodiodes usually have a slower response time as their surface area increases. The common, traditional solar cell used to generate electric solar power is a large area photodiode.

In photography, bracketing is the general technique of taking several shots of the same subject using different camera settings. Bracketing is useful and often recommended in situations that make it difficult to obtain a satisfactory image with a single shot, especially when a small variation in exposure parameters has a comparatively large effect on the resulting image. Given the time it takes to accomplish multiple shots, it is typically, but not always, used for static subjects. Autobracketing is a feature of many modern cameras. When set, it will automatically take several bracketed shots, rather than the photographer altering the settings by hand between each shot.

Noise reduction is the process of removing noise from a signal. Noise reduction techniques exist for audio and images. Noise reduction algorithms may distort the signal to some degree.

The Foveon X3 sensor is a digital camera image sensor designed by Foveon, Inc., and manufactured by Dongbu Electronics. It uses an array of photosites that consist of three vertically stacked photodiodes. Each of the three stacked photodiodes has a different spectral sensitivity, allowing it to respond differently to different wavelengths. The signals from the three photodiodes are then processed as additive color data that are transformed to a standard RGB color space.

Leica Digilux 1

The Leica Digilux 1 was released in 2002, roughly the same time as the Canon G2 and the Nikon 2000. It is the second of Leica's digital offerings. Where the original Digilux was developed in partnership with Fuji Camera, the Digilux 1 was developed in partnership with Panasonic with whom Leica continues to partner in sharing technologies—Leica shares their ability to design superb lenses, and Panasonic designs the camera electronics. According to Leica, this allows both companies to design cameras that creates a harmonious matching of lens to sensor to produce color and contrast to Leica standards.

Crop factor

In digital photography, the crop factor, format factor, or focal length multiplier of an image sensor format is the ratio of the dimensions of a camera's imaging area compared to a reference format; most often, this term is applied to digital cameras, relative to 35 mm film format as a reference. In the case of digital cameras, the imaging device would be a digital sensor. The most commonly used definition of crop factor is the ratio of a 35 mm frame's diagonal (43.3 mm) to the diagonal of the image sensor in question; that is, CF=diag35mm / diagsensor. Given the same 3:2 aspect ratio as 35mm's 36 mm × 24 mm area, this is equivalent to the ratio of heights or ratio of widths; the ratio of sensor areas is the square of the crop factor.

A camera raw image file contains minimally processed data from the image sensor of either a digital camera, a motion picture film scanner, or other image scanner. Raw files are named so because they are not yet processed and therefore are not ready to be printed or edited with a bitmap graphics editor. Normally, the image is processed by a raw converter in a wide-gamut internal color space where precise adjustments can be made before conversion to a "positive" file format such as TIFF or JPEG for storage, printing, or further manipulation. There are dozens of raw formats in use by different manufacturers of digital image capture equipment.

Digital photography Photography with a digital camera

Digital photography uses cameras containing arrays of electronic photodetectors to produce images focused by a lens, as opposed to an exposure on photographic film. The captured images are digitized and stored as a computer file ready for further digital processing, viewing, electronic publishing, or digital printing.

Image sensor Device that converts an optical image into an electronic signal

An image sensor or imager is a sensor that detects and conveys information used to make an image. It does so by converting the variable attenuation of light waves into signals, small bursts of current that convey the information. The waves can be light or other electromagnetic radiation. Image sensors are used in electronic imaging devices of both analog and digital types, which include digital cameras, camera modules, camera phones, optical mouse devices, medical imaging equipment, night vision equipment such as thermal imaging devices, radar, sonar, and others. As technology changes, electronic and digital imaging tends to replace chemical and analog imaging.

Noise (electronics) Random fluctuation in an electrical signal

In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects.

Active-pixel sensor

An active-pixel sensor (APS) is an image sensor where each pixel sensor unit cell has a photodetector and one or more active transistors. In a metal–oxide–semiconductor (MOS) active-pixel sensor, MOS field-effect transistors (MOSFETs) are used as amplifiers. There are different types of APS, including the early NMOS APS and the much more common complementary MOS (CMOS) APS, also known as the CMOS sensor, which is widely used in digital camera technologies such as cell phone cameras, web cameras, most modern digital pocket cameras, most digital single-lens reflex cameras (DSLRs), and mirrorless interchangeable-lens cameras (MILCs). CMOS sensors emerged as an alternative to charge-coupled device (CCD) image sensors and eventually outsold them by the mid-2000s.

Film grain

Film grain or granularity is the random optical texture of processed photographic film due to the presence of small particles of a metallic silver, or dye clouds, developed from silver halide that have received enough photons. While film grain is a function of such particles it is not the same thing as such. It is an optical effect, the magnitude of which depends on both the film stock and the definition at which it is observed. It can be objectionably noticeable in an over-enlarged film photograph.

Exposing to the right

In digital photography, exposing to the right (ETTR) is the technique of adjusting the exposure of an image as high as possible at base ISO to collect the maximum amount of light and thus get the optimum performance out of the digital image sensor.

The merits of digital versus film photography were considered by photographers and filmmakers in the early 21st century after consumer digital cameras became widely available. Digital photography and digital cinematography have both advantages and disadvantages relative to still film and motion picture film photography. In the 21st century, photography came to be predominantly digital, but traditional photochemical methods continue to serve many users and applications.

Dark-frame subtraction

In digital photography, dark-frame subtraction is a way to reduce image noise in photographs shot with long exposure times, at high ISO sensor sensitivity or at high temperatures. It takes advantage of the fact that two components of image noise, dark current and fixed-pattern noise, are the same from shot to shot. Noise from the image sensor include hot pixels, which light up more brightly than surrounding pixels. The technique works by taking a picture with the shutter closed and subtracting that electronically from the original photo exhibiting the noise.

Image sensor format

In digital photography, the image sensor format is the shape and size of the image sensor.

Image processor Specialized digital signal processor used for image processing

An image processor, also known as an image processing engine, image processing unit (IPU), or image signal processor (ISP), is a type of media processor or specialized digital signal processor (DSP) used for image processing, in digital cameras or other devices. Image processors often employ parallel computing even with SIMD or MIMD technologies to increase speed and efficiency. The digital image processing engine can perform a range of tasks. To increase the system integration on embedded devices, often it is a system on a chip with multi-core processor architecture.

An oversampled binary image sensor is an image sensor with non-linear response capabilities reminiscent of traditional photographic film. Each pixel in the sensor has a binary response, giving only a one-bit quantized measurement of the local light intensity. The response function of the image sensor is non-linear and similar to a logarithmic function, which makes the sensor suitable for high dynamic range imaging.

In signal processing, noise is a general term for unwanted modifications that a signal may suffer during capture, storage, transmission, processing, or conversion.

References

  1. Stroebel, Leslie; Zakia, Richard D. (1995). The Focal encyclopedia of photography. Focal Press. p. 507. ISBN   978-0-240-51417-8.
  2. Rohankar, Jayant (Nov 2013). "SURVEY ON VARIOUS NOISES AND TECHNIQUES FOR DENOISING THE COLOR IMAGE" (PDF). International Journal of Application or Innovation in Engineering & Management. 2 (11). Retrieved 15 May 2015.
  3. Philippe Cattin (2012-04-24). "Image Restoration: Introduction to Signal and Image Processing". MIAC, University of Basel. Retrieved 11 October 2013.
  4. Jun Ohta (2008). Smart CMOS Image Sensors and Applications. CRC Press. ISBN   978-0-8493-3681-2.
  5. Junichi Nakamura (2005). Image Sensors and Signal Processing for Digital Still Cameras. CRC Press. ISBN   0-8493-3545-0.
  6. 1 2 3 Lindsay MacDonald (2006). Digital Heritage. Butterworth-Heinemann. ISBN   0-7506-6183-6.
  7. Mehdi Mafi, Harold Martin, Jean Andrian, Armando Barreto, Mercedes Cabrerizo, Malek Adjouadi, “A Comprehensive Survey on Impulse and Gaussian Denoising Filters for Digital Images,” Signal Processing, vol. 157, pp. 236-260, 2019.
  8. 1 2 3 Rafael C. Gonzalez; Richard E. Woods (2007). Digital Image Processing. Pearson Prenctice Hall. ISBN   978-0-13-168728-8.
  9. Alan C. Bovik (2005). Handbook of Image and Video Processing. Academic Press. ISBN   0-12-119792-1.
  10. Linda G. Shapiro; George C. Stockman (2001). Computer Vision. Prentice-Hall. ISBN   0-13-030796-3.
  11. 1 2 3 Boncelet, Charles (2005). "Image Noise Models". In Alan C. Bovik (ed.). Handbook of Image and Video Processing. Academic Press. ISBN   0-12-119792-1.
  12. Mehdi Mafi, Hoda Rajaei, Mercedes Cabrerizo, Malek Adjouadi, “A Robust Edge Detection Approach in the Presence of High Impulse Intensity through Switching Adaptive Median and Fixed Weighted Mean Filtering,” IEEE Transactions on Image Processing, vol. 27, issue. 11, 2018, pp. 5475-5490.
  13. Charles Boncelet (2005), Alan C. Bovik. Handbook of Image and Video Processing. Academic Press. ISBN   0-12-119792-1
  14. Janesick, James R. (2001). Scientific Charge-coupled Devices. SPIE Press. ISBN   0-8194-3698-4.
  15. 1 2 Michael A. Covington (2007). Digital SLR Astrophotography. Cambridge University Press. ISBN   978-0-521-70081-8.
  16. R. E. Jacobson; S. F. Ray; G. G. Attridge; N. R. Axford (2000). The Manual of Photography. Focal Press. ISBN   0-240-51574-9.
  17. Thomas S. Huang (1986). Advances in Computer Vision and Image Processing. JAI Press. ISBN   0-89232-460-0.
  18. Brian W. Keelan; Robert E. Cookingham (2002). Handbook of Image Quality. CRC Press. ISBN   0-8247-0770-2.
  19. Joseph G. Pellegrino; et al. (2006). "Infrared Camera Characterization". In Joseph D. Bronzino (ed.). Biomedical Engineering Fundamentals. CRC Press. ISBN   0-8493-2122-0.
  20. McHugh, Sean. "Digital Cameras: Does Pixel Size Matter? Part 2: Example Images using Different Pixel Sizes (Does Sensor Size Matter?)" . Retrieved 2010-06-03.
  21. 1 2 Martinec, Emil (2008-05-22). "Noise, Dynamic Range and Bit Depth in Digital SLRs (read noise)" . Retrieved 2020-11-24.
  22. R. N., Clark (2008-12-22). "Digital Cameras: Does Pixel Size Matter? Part 2: Example Images using Different Pixel Sizes (Does Sensor Size Matter?)" . Retrieved 2010-06-03.
  23. Wrotniak, J. Anderzej (2009-02-26). "Four Thirds Sensor Size and Aspect Ratio" . Retrieved 2010-06-03.
  24. Singh, Akansha; Singh, K.K. (2012). Digital Image Processing. Umesh Publications. ISBN   978-93-80117-60-7.
  25. Priyadarshini, Neha; Sarkar, Mukul (January 2021). "A 2e rms − Temporal Noise CMOS Image Sensor With In-Pixel 1/ f Noise Reduction and Conversion Gain Modulation for Low Light Imaging". IEEE Transactions on Circuits and Systems I: Regular Papers. 68 (1): 185–195. doi:10.1109/TCSI.2020.3034377. ISSN   1549-8328.
  26. Chervyakov, Nikolay; Lyakhov, Pavel; Nagornov, Nikolay (2020-02-11). "Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for 3D Medical Imaging". Applied Sciences. 10 (4): 1223. doi:10.3390/app10041223. ISSN   2076-3417.
  27. "Astrophotography, Pixel-by-Pixel: Part 1 - Well Depth, Pixel Size, and Quantum Efficiency" . Retrieved 2020-11-24.|first= missing |last= (help)
  28. Clark, Roger N. (2012-07-04). "Exposure and Digital Cameras, Part 1. What is ISO on a digital camera? When is a camera ISOless? ISO Myths and Digital Cameras" . Retrieved 2020-11-24.
  29. Martinec, Emil (2008-05-22). "Noise, Dynamic Range and Bit Depth in Digital SLRs (S/N ratio vs. exposure, and Dynamic Range)" . Retrieved 2020-11-24.
  30. Martinec, Emil (2008-05-22). "Noise, Dynamic Range and Bit Depth in Digital SLRs (S/N and Exposure Decisions)" . Retrieved 2020-11-24.