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Example of 3 median filters of varying radiuses applied to the same noisy photograph. The median filter is a non-linear digital filtering technique, often used to remove noise from an image, [1] signal, [2] and video. [3] Such noise reduction is a typical pre-processing step to improve the results of later processing (for example, edge ...
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. Noise rejection is the ability of a circuit to isolate an undesired signal component from the desired signal component, as with common-mode rejection ratio.
Almost every technique and device for signal processing has some connection to noise. Some random examples are: Noise shaping; Antenna analyzer or noise bridge, used to measure the efficiency of antennas; Noise gate; Noise generator, a circuit that produces a random electrical signal; Radio noise source used to calibrate radiotelescopes
For example, the Wiener filter can be used in image processing to remove noise from a picture. For example, using the Mathematica function: WienerFilter[image,2] on the first image on the right, produces the filtered image below it. It is commonly used to denoise audio signals, especially speech, as a preprocessor before speech recognition.
This output can be converted to a signal by passing it through a digital-to-analog converter. There are problems with noise introduced by the conversions, but these can be controlled and limited for many useful filters. Due to the sampling involved, the input signal must be of limited frequency content or aliasing will occur.
The regularization parameter plays a critical role in the denoising process. When =, there is no smoothing and the result is the same as minimizing the sum of squares.As , however, the total variation term plays an increasingly strong role, which forces the result to have smaller total variation, at the expense of being less like the input (noisy) signal.
Here, / is the inverse of the original system, = / is the signal-to-noise ratio, and | | is the ratio of the pure filtered signal to noise spectral density. When there is zero noise (i.e. infinite signal-to-noise), the term inside the square brackets equals 1, which means that the Wiener filter is simply the inverse of the system, as we might ...
Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways: . curve fitting often involves the use of an explicit function form for the result, whereas the immediate results from smoothing are the "smoothed" values with no later use made of a functional form if there is one;