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The transformation is called "whitening" because it changes the input vector into a white noise vector. Several other transformations are closely related to whitening: the decorrelation transform removes only the correlations but leaves variances intact, the standardization transform sets variances to 1 but leaves correlations intact,
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.
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.
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.
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 ...
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 ...
The evidence for a step is tested by statistical procedures, for example, by use of the two-sample Student's t-test. Alternatively, a nonlinear filter such as the median filter is applied to the signal. Filters such as these attempt to remove the noise whilst preserving the abrupt steps.
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;