Noise reduction

Noise reduction is the process of removing

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.[1]

In seismic exploration

Boosting signals in seismic data is especially crucial for

Noise reduction example

Example of noise reduction using Audacity with 0 dB, 5 dB, 12 dB, and 30 dB reduction, 150 Hz frequency smoothing, and 0.15 seconds attack/decay time.

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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 that dither systems actually add noise to a signal to improve its quality.

Compander-based noise reduction systems

Dual-ended

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). 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 with Henry 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.

The

Dynamic noise limiter (DNL) is an audio noise reduction system originally introduced by Philips in 1971 for use on cassette decks.^[11] Its circuitry is also based on a single chip.^[23][24]

It was further developed into dynamic noise reduction (DNR) by National Semiconductor to reduce noise levels on long-distance telephony.^[25] First sold in 1981, DNR is frequently confused with the far more common Dolby noise-reduction system.^[26]

Unlike Dolby and

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.[31]^{[page needed]} 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 or wanted noise, will be untouched. The region is typically defined by the location of the signal's instantaneous frequency,^[32] as most of the signal energy to be preserved is concentrated about it.

Software programs

Most digital audio workstations (DAWs) and audio editing software have one or more noise reduction functions.

In images

Images taken with

In Gaussian noise,^[35] 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

Removal

Tradeoffs

There are many noise reduction algorithms in image processing.^[36] 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 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 smear across the area. Because of this blurring, linear filters are seldom used in practice for noise reduction;^{[citation needed]} 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;^[37] 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^[38] and feature preservation^[39] using the wavelet filter banks.^[40] 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.^[41] Therefore, the first wavelet-based denoising methods were based on thresholding of detail subband coefficients.^{[42][page needed]} 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.^[41]

Statistical methods

Statistical methods for image denoising exist as well. 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 ${\displaystyle \delta _{i}}$ denote the pixels adjacent to the ${\displaystyle i}$th pixel. Then the

${\displaystyle [0,1]}$

${\displaystyle i}$

${\displaystyle \mathbb {P} (x(i)=c|x(j)\forall j\in \delta i)\propto e^{-{\frac {\beta }{2\lambda }}\sum _{j\in \delta i}(c-x(j))^{2}}}$

for a chosen parameter ${\displaystyle \beta \geq 0}$ and variance ${\displaystyle \lambda }$. 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.^[43][44]

Block-matching algorithms

A

• Filter (signal processing)
• Signal processing
• Signal subspace

Audio

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

Images and video

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

Similar problems

• Deblurring

References