Noise reduction

For the reduction of a sound's volume, seeSoundproofing.For the noise reduction of machinery and products, seeNoise control.

Noise reductionis the process of removingnoisefrom asignal.Noise reduction techniques exist for audio and images. Noise reduction algorithms maydistortthe signal to some degree.Noise rejectionis the ability of a circuit to isolate an undesired signal component from the desired signal component, as withcommon-mode rejection ratio.

Allsignal processingdevices, bothanaloganddigital,have traits that make them susceptible to noise. Noise can be random with an even frequency distribution (white noise), or frequency-dependent noise introduced by a device's mechanism or signal processingalgorithms.

Inelectronic systems,a major type of noise ishisscreated by random electron motion due to thermal agitation. These agitated electrons rapidly add and subtract from the output signal and thus create detectablenoise.

In the case ofphotographic filmandmagnetic 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 (usuallyferric oxideormagnetite), 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.

In general

Noise reduction algorithms tend to alter signals to a greater or lesser degree. The local signal-and-noise orthogonalization algorithm can be used to avoid changes to the signals.

In seismic exploration

Boosting signals in seismic data is especially crucial forseismic imaging,inversion,and interpretation,thereby greatly improving the success rate in oil & gas exploration.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

Tape hissis a performance-limiting issue inanalog tape recording.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 thetape heads.

Four types of noise reduction exist: single-ended pre-recording, single-ended hiss reduction, single-endedsurface noisereduction, and codec or dual-ended systems. Single-ended pre-recording systems (such asDolby HX Pro), work to affect the recording medium at the time of recording. Single-ended hiss reduction systems (such asDNLorDNR) 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 asCEDARand the earlier SAE 5000A,BurwenTNE 7000, andPackburn101/323/323A/323AA and 325) is applied to the playback ofphonograph recordsto address scratches, pops, and surface non-linearities. Single-endeddynamic range expanderslike thePhase LinearAutocorrelator Noise Reduction and Dynamic Range Recovery System (Models 1000 and 4000) can reduce various noise from old recordings. Dual-ended systems (such asDolby noise-reduction systemordbx) have a pre-emphasis process applied during recording and then a de-emphasis process applied during playback.

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

Compander-based noise reduction systems

Dual-endedcompandernoise reduction systems have a pre-emphasis process applied during recording and then a de-emphasis process applied at playback. Systems include the professional systemsDolby AandDolby SRbyDolby Laboratories,dbx Professionalanddbx Type Ibydbx,Donald Aldous'EMTNoiseBX,Burwen Noise Eliminator,Telefunken'stelcom c4and MXR Innovations' MXRas well as the consumer systemsDolby NR,Dolby B,Dolby CandDolby S,dbx Type II,Telefunken'sHigh ComandNakamichi'sHigh-Com II,Toshiba's (Aurex AD-4)adres,JVC'sANRSandSuper ANRS,Fisher/Sanyo'sSuper D,SNRS,and the Hungarian/East-GermanEx-Kosystem.

In some compander systems, the compression is applied during professional media production and only the expansion is applied by the listener; for example, systems likedbx disc,High-Com II,CX 20andUCused for vinyl recordings andDolby FM,High Com FMandFMXused in FM radio broadcasting.

The first widely used audio noise reduction technique was developed byRay Dolbyin 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). 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 (developed in conjunction withHenry Kloss) was a single-band system designed for consumer products. The Dolby B system, while not as effective as Dolby A, had the advantage of remaining listenable on playback systems without a decoder.

TheTelefunkenHigh Comintegrated circuitU401BRcould be utilized to work as a mostlyDolby B–compatible compander as well.In various late-generation High Com tape decks the Dolby-B emulatingD NR Expanderfunctionality worked not only for playback, but, as an undocumented feature, also during recording.

dbxwas a competing analog noise reduction system developed byDavid E. Blackmer,founder ofDbx, Inc.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 without a decoder. However, it could achieve up to 30 dB of noise reduction.

Since analogvideo recordingsuse frequency modulation for the luminance part (composite video signal in direct color 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 byPhilipsin 1971 for use oncassette decks.Its circuitry is also based on a singlechip.

It was further developed intodynamic noise reduction(DNR) byNational Semiconductorto reduce noise levels on long-distancetelephony.First sold in 1981, DNR is frequently confused with the far more commonDolby noise-reduction system.

Unlike Dolby anddbx Type IandType IInoise reduction systems, DNL and DNR are playback-only signal processing systems that do not require the source material to first be encoded. They can be used to remove background noise from any audio signal, includingmagnetic taperecordings andFM radiobroadcasts, reducing noise by as much as 10 dB.They can also 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.

One of DNR's first widespread applications was in theGMDelcocar stereosystems in US GM cars introduced in 1984.It was also used in factory car stereos inJeepvehicles in the 1980s, such as theCherokee XJ.Today, DNR, DNL, and similar systems are most commonly encountered as a noise reduction system in microphone systems.

Other approaches

A second class of algorithms work in the time-frequency domain using somelinearornonlinear filtersthat have local characteristics and are often calledtime-frequency filters.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 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 orwanted noise,will be untouched. The region is typically defined by the location of the signal's instantaneous frequency,as most of the signal energy to be preserved is concentrated about it.

Yet another approach is the automatic noise limiter andnoise blankercommonly found onHAM radiotransceivers,CB radiotransceivers, etc. Both of the aforementioned filters can be used separately, or in conjunction with each other at the same time, depending on the transceiver itself.

Software programs

Mostdigital audio workstations(DAWs) andaudio editing softwarehave one or more noise reduction functions.

In images

Images taken withdigital camerasor conventionalfilm cameraswill pick up noise from a variety of sources. Further use of these images will often require that the noise be reduced either for aesthetic purposes, or for practical purposes such ascomputer vision.

Types

Insalt and pepper noise(sparse light and dark disturbances),also known as impulse noise,pixelsin 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. When viewed, the image contains dark and white dots, hence the term salt and pepper noise. Generally, this type of noise will only affect a small number of image pixels. Typical sources include flecks of dust inside the camera and overheated or faultyCCDelements.

InGaussian 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 anormal distributionof noise. While other distributions are possible, the Gaussian (normal) distribution is usually a good model, due to thecentral limit theoremthat 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 beingindependent and identically distributed,and hence uncorrelated.

Removal

Tradeoffs

There are many noise reduction algorithms in image processing.In selecting a noise reduction algorithm, one must weigh several factors:

• the available computer power and time available: a digital camera must apply noise reduction in a fraction of a second using a tiny onboard CPU, while a desktop computer has much more power and time
• whether sacrificing some real detail is acceptable if it allows more noise to be removed (how aggressively to decide whether variations in the image are noise or not)
• the characteristics of the noise and the detail in the image, to better make those decisions

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). Most photographic noise reduction algorithms split the image detail into chroma and luminance components and apply more noise reduction to the former or allows the user to control chroma and luminance noise reduction separately.

Linear smoothing filters

One method to remove noise is byconvolvingthe original image with a mask that represents alow-pass filteror smoothing operation. For example, the Gaussian mask comprises elements determined by aGaussian 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; theGaussian filteris 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 neighborhoodsmearacross 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 smoothingpartial differential equationsimilar to theheat equation,which is calledanisotropic diffusion.With a spatially constant diffusion coefficient, this is equivalent to theheat equationor linearGaussian 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

Main article:Non-local means

Another approach for removing noise is based onnon-localaveraging 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

Amedian filteris an example of a nonlinear 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 themedianvalue 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;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 reductionand feature preservationusing the wavelet filter banks.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.Therefore, the first wavelet-based denoising methods were based on thresholding of detail subband coefficients.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, nonlinear 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.

Statistical methods

Statistical methods for image denoising exist as well. ForGaussian noise,one can model the pixels in a greyscale image as auto-normally distributed, where each pixel'struegreyscale value is normally distributed with mean equal to the average greyscale value of its neighboring pixels and a given variance.

Let$\delta _{i}$denote the pixels adjacent to the$i$th pixel. Then theconditional distributionof the greyscale intensity (on a$[0,1]$scale) at the$i$th node is:

$\mathbb {P} {\big (}x(i)=c\mid x(j)\,\forall j\in \delta _{i}{\big )}\propto \exp \left({-{\frac {\beta }{2\lambda }}\sum _{j\in \delta _{i}}{\big (}c-x(j){\big )}^{2}}\right)$

for a chosen parameter$\beta \geq 0$and variance$\lambda$.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.

Block-matching algorithms

Main article:Block-matching and 3D filtering

Ablock-matching algorithmcan be applied to group similar image fragments of overlappingmacroblocksof identical size. Stacks of similar macroblocks are then filtered together in the transform domain and each image fragment is finally restored to its original location using a weighted average of the overlapping pixels.

Random field

Main article:Shrinkage Fields (image restoration)

Shrinkage fieldsis arandom field-basedmachine learningtechnique that brings performance comparable to that ofBlock-matching and 3D filteringyet requires much lower computational overhead such that it can be performed directly withinembedded systems.

Deep learning

Variousdeep learningapproaches have been proposed to achieve noise reductionand suchimage restorationtasks.Deep Image Prioris one such technique that makes use ofconvolutional neural networkand is notable in that it requires no prior training data.

Software

Most general-purpose image and photo editing software will have one or more noise-reduction functions (median,blur,despeckle, etc.).

See also

General noise issues

• Filter (signal processing)
• Signal subspace

Audio

• Architectural acousticsincludingSoundproofing
• Click removal
• Codec listening test
• Noise blanker
• Noise print
• Noise-cancelling headphones
• Sound masking

Images and video

• Dark-frame subtraction
• Digital image processing
• Total variation denoising
• Video denoising

Similar problems

• Deblurring

External links

• Recent trends in denoising tutorial
• Noise Reduction in photography