Noise reduction

Noise reduction is the process of removing noise from a signal.

All recording devices, both analog and digital, have traits that make them susceptible to noise. Noise can be random or white noise with no coherence, or coherent noise introduced by the device's mechanism or processing algorithms.

In electronic recording devices, a major form of noise is hiss caused by random electrons that, heavily influenced by heat, stray from their designated path. These stray electrons influence the voltage of the output signal and thus create detectable noise.

In the case of photographic film and magnetic tape, noise (both visible and audible) is introduced due to the grain structure of the medium. In photographic film, the size of the grains in the film determines the film's sensitivity, more sensitive film having larger sized grains. In magnetic tape, the larger the grains of the magnetic particles (usually ferric oxide or magnetite), the more prone the medium is to noise.

To compensate for this, larger areas of film or magnetic tape may be used to lower the noise to an acceptable level.

Many noise reduction algorithms tend to damage more or less signals. The local signal-and-noise orthogonalization algorithm [1] can be used to avoid the damages to signals.

In seismic exploration

Boosting signals in seismic data is especially crucial for seismic imaging,[2][3] inversion,[4][5] and interpretation,[6] thereby greatly improving the success rate in oil & gas exploration.[7][8][9][10] The useful signal that is smeared in the ambient random noise is often neglected and thus may cause fake discontinuity of seismic events and artifacts in the final migrated image. Enhancing the useful signal while preserving edge properties of the seismic profiles by attenuating random noise can help reduce interpretation difficulties and misleading risks for oil and gas detection.

In audio

When using analog tape recording technology, they may exhibit a type of noise known as tape hiss. This is related to the particle size and texture used in the magnetic emulsion that is sprayed on the recording media, and also to the relative tape velocity across the tape heads.

Four types of noise reduction exist: single-ended pre-recording, single-ended hiss reduction, single-ended surface noise reduction, and codec or dual-ended systems. Single-ended pre-recording systems (such as Dolby HX Pro) work to affect the recording medium at the time of recording. Single-ended hiss reduction systems (such as DNL or DNR) work to reduce noise as it occurs, including both before and after the recording process as well as for live broadcast applications. Single-ended surface noise reduction (such as CEDAR and the earlier SAE 5000A and Burwen TNE 7000) is applied to the playback of phonograph records to attenuate the sound of scratches, pops, and surface non-linearities. Dual-ended systems (such as Dolby B, Dolby C, Dolby S, dbx Type I and dbx Type II, High Com and High Com II as well as Toshiba's adres and JVC's ANRS) have a pre-emphasis process applied during recording and then a de-emphasis process applied at playback.

Dolby and dbx noise reduction system

While there are dozens of different kinds of noise reduction, the first widely used audio noise reduction technique was developed by Ray Dolby in 1966. Intended for professional use, Dolby Type A was an encode/decode system in which the amplitude of frequencies in four bands was increased during recording (encoding), then decreased proportionately during playback (decoding). The Dolby B system (developed in conjunction with Henry Kloss) was a single band system designed for consumer products. In particular, when recording quiet parts of an audio signal, the frequencies above 1 kHz would be boosted. This had the effect of increasing the signal to noise ratio on tape up to 10 dB depending on the initial signal volume. When it was played back, the decoder reversed the process, in effect reducing the noise level by up to 10 dB. The Dolby B system, while not as effective as Dolby A, had the advantage of remaining listenable on playback systems without a decoder.

Dbx was the competing analog noise reduction system developed by David E. Blackmer, founder of dbx laboratories.[11] It used a root-mean-squared (RMS) encode/decode algorithm with the noise-prone high frequencies boosted, and the entire signal fed through a 2:1 compander. Dbx operated across the entire audible bandwidth and unlike Dolby B was unusable as an open ended system. However it could achieve up to 30 dB of noise reduction.

Since Analog video recordings use frequency modulation for the luminance part (composite video signal in direct colour systems), which keeps the tape at saturation level, audio style noise reduction is unnecessary.

Dynamic noise limiter and dynamic noise reduction

Dynamic noise limiter (DNL) is an audio noise reduction system originally introduced by Philips in 1971 for use on cassette decks. Its circuitry is also based on a single chip.[12]

It was further developed into dynamic noise reduction (DNR) by National Semiconductor to reduce noise levels on long-distance telephony.[13] First sold in 1981, DNR is frequently confused with the far more common Dolby noise reduction system.[14] However, unlike Dolby and dbx Type I & Type II noise reduction systems, DNL and DNR are playback-only signal processing systems that do not require the source material to first be encoded, and they can be used together with other forms of noise reduction.[15]

Because DNL and DNR are non-complementary, meaning they do not require encoded source material, they can be used to remove background noise from any audio signal, including magnetic tape recordings and FM radio broadcasts, reducing noise by as much as 10 dB.[16] They can be used in conjunction with other noise reduction systems, provided that they are used prior to applying DNR to prevent DNR from causing the other noise reduction system to mistrack.

The Telefunken High Com integrated circuit U401BR could be utilized to work as a Dolby B–compatible DNR-style expander as well.[17]

One of DNR's first widespread applications was in the GM Delco car stereo systems in U.S. GM cars introduced in 1984.[18] It was also used in factory car stereos in Jeep vehicles in the 1980s, such as the Cherokee XJ. Today, DNR, DNL, and similar systems are most commonly encountered as a noise reduction system in microphone systems.[19]

Other approaches

A second class of algorithms work in the time-frequency domain using some linear or non-linear filters that have local characteristics and are often called time-frequency filters.[20] Noise can therefore be also removed by use of spectral editing tools, which work in this time-frequency domain, allowing local modifications without affecting nearby signal energy. This can be done manually by using the mouse with a pen that has a defined time-frequency shape. This is done much like in a paint program drawing pictures. Another way is to define a dynamic threshold for filtering noise, that is derived from the local signal, again with respect to a local time-frequency region. Everything below the threshold will be filtered, everything above the threshold, like partials of a voice or "wanted noise", will be untouched. The region is typically defined by the location of the signal Instantaneous Frequency,[21] as most of the signal energy to be preserved is concentrated about it.

Modern digital sound (and picture) recordings no longer need to worry about tape hiss so analog style noise reduction systems are not necessary. However, an interesting twist is that dither systems actually add noise to a signal to improve its quality.

Software programs

Most general purpose voice editing software will have one or more noise reduction functions (Audacity, WavePad, etc.). Special purpose noise reduction software programs include Gnome Wave Cleaner, Sony Creative Noise Reduction, SoliCall Pro, Voxengo Redunoise and X-OOM Music Clean.

In images

Images taken with both digital cameras and conventional film cameras will pick up noise from a variety of sources. Further use of these images will often require that the noise be (partially) removed – for aesthetic purposes as in artistic work or marketing, or for practical purposes such as computer vision.

Types

In salt and pepper noise (sparse light and dark disturbances), pixels in the image are very different in color or intensity from their surrounding pixels; the defining characteristic is that the value of a noisy pixel bears no relation to the color of surrounding pixels. Generally this type of noise will only affect a small number of image pixels. When viewed, the image contains dark and white dots, hence the term salt and pepper noise. Typical sources include flecks of dust inside the camera and overheated or faulty CCD elements.

In Gaussian noise, each pixel in the image will be changed from its original value by a (usually) small amount. A histogram, a plot of the amount of distortion of a pixel value against the frequency with which it occurs, shows a normal distribution of noise. While other distributions are possible, the Gaussian (normal) distribution is usually a good model, due to the central limit theorem that says that the sum of different noises tends to approach a Gaussian distribution.

In either case, the noise at different pixels can be either correlated or uncorrelated; in many cases, noise values at different pixels are modeled as being independent and identically distributed, and hence uncorrelated.

Removal

Tradeoffs

In selecting a noise reduction algorithm, one must weigh several factors:

Chroma and luminance noise separation

In real-world photographs, the highest spatial-frequency detail consists mostly of variations in brightness ("luminance detail") rather than variations in hue ("chroma detail"). Since any noise reduction algorithm should attempt to remove noise without sacrificing real detail from the scene photographed, one risks a greater loss of detail from luminance noise reduction than chroma noise reduction simply because most scenes have little high frequency chroma detail to begin with. In addition, most people find chroma noise in images more objectionable than luminance noise; the colored blobs are considered "digital-looking" and unnatural, compared to the grainy appearance of luminance noise that some compare to film grain. For these two reasons, most photographic noise reduction algorithms split the image detail into chroma and luminance components and apply more noise reduction to the former.

Most dedicated noise-reduction computer software allows the user to control chroma and luminance noise reduction separately.

Linear smoothing filters

One method to remove noise is by convolving the original image with a mask that represents a low-pass filter or smoothing operation. For example, the Gaussian mask comprises elements determined by a Gaussian function. This convolution brings the value of each pixel into closer harmony with the values of its neighbors. In general, a smoothing filter sets each pixel to the average value, or a weighted average, of itself and its nearby neighbors; the Gaussian filter is just one possible set of weights.

Smoothing filters tend to blur an image, because pixel intensity values that are significantly higher or lower than the surrounding neighborhood would "smear" across the area. Because of this blurring, linear filters are seldom used in practice for noise reduction; they are, however, often used as the basis for nonlinear noise reduction filters.

Anisotropic diffusion

Another method for removing noise is to evolve the image under a smoothing partial differential equation similar to the heat equation, which is called anisotropic diffusion. With a spatially constant diffusion coefficient, this is equivalent to the heat equation or linear Gaussian filtering, but with a diffusion coefficient designed to detect edges, the noise can be removed without blurring the edges of the image.

Non-local means

Another approach for removing noise is based on non-local averaging of all the pixels in an image. In particular, the amount of weighting for a pixel is based on the degree of similarity between a small patch centered on that pixel and the small patch centered on the pixel being de-noised.

Nonlinear filters

A median filter is an example of a non-linear filter and, if properly designed, is very good at preserving image detail. To run a median filter:

  1. consider each pixel in the image
  2. sort the neighbouring pixels into order based upon their intensities
  3. replace the original value of the pixel with the median value from the list

A median filter is a rank-selection (RS) filter, a particularly harsh member of the family of rank-conditioned rank-selection (RCRS) filters;[22] a much milder member of that family, for example one that selects the closest of the neighboring values when a pixel's value is external in its neighborhood, and leaves it unchanged otherwise, is sometimes preferred, especially in photographic applications.

Median and other RCRS filters are good at removing salt and pepper noise from an image, and also cause relatively little blurring of edges, and hence are often used in computer vision applications.

Wavelet transform

The main aim of an image denoising algorithm is to achieve both noise reduction and feature preservation. In this context, wavelet-based methods are of particular interest. In the wavelet domain, the noise is uniformly spread throughout coefficients while most of the image information is concentrated in a few large ones.[23] Therefore, the first wavelet-based denoising methods were based on thresholding of detail subbands coefficients.[24] However, most of the wavelet thresholding methods suffer from the drawback that the chosen threshold may not match the specific distribution of signal and noise components at different scales and orientations.

To address these disadvantages, non-linear estimators based on Bayesian theory have been developed. In the Bayesian framework, it has been recognized that a successful denoising algorithm can achieve both noise reduction and feature preservation if it employs an accurate statistical description of the signal and noise components.[23]

Statistical methods

Statistical methods for image denoising exist as well, though they are infrequently used as they are computationally demanding. For Gaussian noise, one can model the pixels in a greyscale image as auto-normally distributed, where each pixel's "true" greyscale value is normally distributed with mean equal to the average greyscale value of its neighboring pixels and a given variance.

Let denote the pixels adjacent to the th pixel. Then the conditional distribution of the greyscale intensity (on a scale) at the th node is:

for a chosen parameter and variance . One method of denoising that uses the auto-normal model uses the image data as a Bayesian prior and the auto-normal density as a likelihood function, with the resulting posterior distribution offering a mean or mode as a denoised image.[25]

Software programs

Most general purpose image and photo editing software will have one or more noise reduction functions (median, blur, despeckle, etc.). Special purpose noise reduction software programs include Neat Image, Noiseless, Noiseware, Noise Ninja, G'MIC (through the -denoise command), and pnmnlfilt (nonlinear filter) found in the open source Netpbm tools. General purpose image and photo editing software including noise reduction functions include Adobe Photoshop, GIMP, PhotoImpact, Paint Shop Pro, Helicon Filter, and Darktable.[26]

See also

General noise issues

Audio

Video

Similar problems

References

  1. ↑ Chen, Yangkang; Fomel, Sergey (November–December 2015). "Random noise attenuation using local signal-and-noise orthogonalization". Geophysics. 80 (6): WD1-WD9. doi:10.1190/GEO2014-0227.1.
  2. ↑ Xue, Zhiguang; Chen, Yangkang; Fomel, Sergey; Sun, Junzhe (2016). "Seismic imaging of incomplete data and simultaneous-source data using least-squares reverse time migration with shaping regularization". Geophysics. 81 (1): S11-S20. doi:10.1190/geo2014-0524.1.
  3. ↑ Chen, Yangkang; Yuan, Jiang; Zu, Shaohuan; Qu, Shan; Gan, Shuwei (2015). "Seismic imaging of simultaneous-source data using constrained least-squares reverse time migration". Journal of Applied Geophysics. 114: 32–35. doi:10.1016/j.jappgeo.2015.01.004.
  4. ↑ Chen, Yangkang; Chen, Hanming; Xiang, Kui; Chen, Xiaohong (2017). "Geological structure guided well log interpolation for high-fidelity full waveform inversion". Geophysical Journal International. 209 (1): 21–31. doi:10.1093/gji/ggw343.
  5. ↑ Gan, Shuwei; Wang, Shoudong; Chen, Yangkang; Qu, Shan; Zu, Shaohuan (2016). "Velocity analysis of simultaneous-source data using high-resolution semblance—coping with the strong noise". Geophysical Journal International. 204: 768–779. doi:10.1093/gji/ggv484.
  6. ↑ Chen, Yangkang (2017). "Probing the subsurface karst features using time-frequency decomposition". Interpretation. 4 (4): T533-T542. doi:10.1190/INT-2016-0030.1.
  7. ↑ Huang, Weilin; Wang, Runqiu; Chen, Yangkang; Li, Huijian; Gan, Shuwei (2016). "Damped multichannel singular spectrum analysis for 3D random noise attenuation". Geophysics. 81 (4): V261-V270. doi:10.1190/geo2015-0264.1.
  8. ↑ Chen, Yangkang (2016). "Dip-separated structural filtering using seislet transform and adaptive empirical mode decomposition based dip filter". Geophysical Journal International. 206: 457–469. doi:10.1093/gji/ggw165.
  9. ↑ Chen, Yangkang; Ma, Jianwei; Fomel, Sergey (2016). "Double-sparsity dictionary for seismic noise attenuation". Geophysics. 81 (4): V261-V270. doi:10.1190/geo2014-0525.1.
  10. ↑ Chen, Yangkang (2017). "Fast dictionary learning for noise attenuation of multidimensional seismic data". Geophysical Journal International. 209 (1): 21–31. doi:10.1093/gji/ggw492.
  11. ↑ Hoffman, F. (2004), Encyclopedia of Recorded Sound, 1 (revised ed.), Taylor & Francis
  12. ↑ "Noise Reduction". Audiotools.com. 2013-11-10.
    https://web.archive.org/web/20081105073059/http://freespace.virgin.net:80/ljmayes.mal/comp/philips.htm. Archived from the original on November 5, 2008. Retrieved January 14, 2009. Missing or empty |title= (help)
  13. ↑ "Dynamic Noise Reduction". ComPol Inc.
  14. ↑ https://web.archive.org/web/20070927190856/http://www.national.com/company/pressroom/history80.html. Archived from the original on September 27, 2007. Retrieved January 14, 2009. Missing or empty |title= (help)
  15. ↑ https://web.archive.org/web/20081220145857/http://triadspeakers.com/education_avterms.html. Archived from the original on December 20, 2008. Retrieved January 14, 2009. Missing or empty |title= (help)
  16. ↑ https://web.archive.org/web/20081220022234/http://www.national.com/pf/LM/LM1894.html. Archived from the original on December 20, 2008. Retrieved January 14, 2009. Missing or empty |title= (help)
  17. ↑ "HIGH COM - The HIGH COM broadband compander utilizing the integrated circuit U 401 BR" (PDF). AEG-Telefunken.
  18. ↑ Ed Gunyo. "Evolution of the Riviera - 1983 the 20th Anniversary". Riviera Owners Association. Originally published in The Riview Vol. 21, No. 6 September/October 2005.
  19. ↑ http://www.hellodirect.com/catalog/Product.jhtml?PRODID=11127&CATID=15295%5B%5D
  20. ↑ B. Boashash, editor, Time-Frequency Signal Analysis and Processing – A Comprehensive Reference, Elsevier Science, Oxford, 2003; ISBN 0-08-044335-4
  21. ↑ B. Boashash, "Estimating and Interpreting the Instantaneous Frequency of a Signal-Part I: Fundamentals", Proceedings of the IEEE, Vol. 80, No. 4, pp. 519–538, April 1992, doi:10.1109/5.135376
  22. ↑ Puyin Liu and Hongxing Li (2004). Fuzzy Neural Network Theory and Application. World Scientific. ISBN 981-238-786-2.
  23. 1 2 M. Forouzanfar, H. Abrishami-Moghaddam, and S. Ghadimi, "Locally adaptive multiscale Bayesian method for image denoising based on bivariate normal inverse Gaussian distributions", International Journal of Wavelets, Multiresolution and Information Processing, vol. 6, Issue 4, pp. 653–64, July 2008.
  24. ↑ Mallat, S.: A Wavelet Tour of Signals Processing. Academic Press, London (1998)
  25. ↑ Julian Besag (1986). "On the Statistical Analysis of Dirty Pictures". Journal of the Royal Statistical Society. Series B (Methodological). 48 (3): 259–302. JSTOR 2345426.
  26. ↑ jo (2012-12-11). "profiling sensor and photon noise .. and how to get rid of it.". darktable.
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