Guys
Salt and pepper noise (scattered light and dark disturbances), occurs when pixels in an image are very different in color or intensity from surrounding pixels; the defining characteristic is that the value of a noisy pixel bears no relation to the color of the surrounding pixels. Generally, this type of noise will only affect a small number of pixels in the image. When viewed, the image contains dark and white dots, hence the name of this phenomenon. Typical sources include dust specks inside the camera and overheated or defective CCD photo pickup elements.
Gaussian noise is when the value of each pixel in the image deviates 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. Although other distributions are possible, the Gaussian (normal) distribution is usually a good model, due to the central limit theorem which says that the sum of different noises tends to approach a Gaussian distribution.
In any case, the noise in different pixels can be correlated or uncorrelated; In many cases, noise values at different pixels are modeled as independent and identically distributed random variables and are therefore uncorrelated.
Elimination
There are numerous noise reduction algorithms in image processing.[34] When selecting a noise reduction algorithm, several factors must be weighed:
• - The available computer power and the time available: a digital camera must apply noise reduction in a fraction of a second using a small integrated CPU, while a desktop computer has much more power and time to perform the necessary calculations.
• - Whether sacrificing some real details is acceptable when it allows you to eliminate more noise (deciding whether variations in the image are noise or not).
• - The characteristics of noise and detail in the image, to better make those decisions.
In real-world photographs, the highest spatial frequency detail consists primarily of variations in brightness ("luminance detail") rather than variations in hue ("chroma detail"). Since any noise reduction algorithm must attempt to remove noise without sacrificing the actual details of the photographed scene, you risk greater loss of detail from luminance noise reduction than from chroma noise reduction simply because most scenes have little high-frequency chroma detail. Additionally, most people find chromatic noise in images more objectionable than luminance noise; Color spots 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 divide image detail into chroma and luminance components; and apply more noise reduction to the first one.
Most computer programs dedicated to noise reduction allow the user to control chrominance and luminance noise reduction separately.
One method to remove noise is by convolving the original image with a mask representing a low-pass filter or smoothing operation. For example, the Gaussian mask comprises elements determined by a Gaussian function. This convolution places the value of each pixel in greater 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 near 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" the area. Because of this blurring, linear filters are rarely used in practice to reduce noise. However, they are often used as the basis for non-linear noise reduction filters.
Another method to remove noise is to subject the image to smoothing based on a partial differential equation similar to the heat equation, which is called anisotropic diffusion. With a spatially constant diffusion coefficient, this is equivalent to filtering using the heat (or linear Gaussian) equation, but with a diffusion coefficient designed to detect edges, noise can be removed without blurring the edges of the image.
Another approach to denoising is based on non-local averaging" of all pixels in an image. In particular, the amount of weighting of 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 when the noise is removed.
A median filter is an example of a nonlinear filter, and if designed correctly, is very good at preserving image detail. To run a median filter:
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- Each pixel of the image is considered.
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- Neighboring pixels are ordered based on their intensities.
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- The original pixel value is replaced with the median value "Median (statistic)") from the list.
This is a range selection (RS) filter, a particularly harsh member of the family of range-conditioned range selection (RCRS) filters;
Median RCRS and other filters are good at removing salt-and-pepper noise from an image and also do relatively little blurring of the edges, and are therefore often used in computer vision applications.
The main goal 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, noise is distributed uniformly across coefficients, while most of the image information is concentrated in a few large wavelets.[36] Therefore, early wavelet-based denoising methods relied on thresholds of detail subband coefficients.[37] However, most wavelet thresholding methods suffer from the drawback that the chosen threshold may not match. with 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[36].
Statistical methods for image denoising also exist, although they are infrequently used as they are computationally demanding. For Gaussian noise, pixels in a grayscale image can be modeled as automatically normally distributed, such that the "true" grayscale value of each pixel is normally distributed with a mean equal to the average grayscale value of its neighboring pixels and according to a given variance.
Let the pixels be adjacent to the th pixel. Then the conditional distribution") of the grayscale intensity (on a scale) at node th is:
for a chosen parameter and variance. A denoising method using the automatic normal model uses the image data with a Bayesian analysis prior and the automatic normal density as a likelihood function, and the resulting posterior distribution provides a mean or mode as a denoised image.[38][39].
A block matching algorithm can be applied to group similar image fragments into overlapping macroblocks of identical size, the stacks of similar macroblocks are filtered together in the transformation domain and each image fragment is finally restored to its original location using a weighted average of the overlapping pixels.[40].
Shrinkage fields&action=edit&redlink=1 "Shrinkage fields (image restoration) (not yet written)") are a machine learning-based random field technique that offers performance comparable to the 3D and block matching filtering method"), but requires much less computational overhead (so it could be performed directly within an embedded system).[41].
Several deep learning approaches have been proposed to solve noise reduction and image restoration tasks. Deep Image Prior") is one of those techniques, which uses convolutional neural networks and is distinguished because it does not require prior training data.[42].