Wiener deconvolution

In mathematics, Wiener deconvolution is an application of the Wiener filter to the noise problems inherent in deconvolution. It works in the frequency domain, attempting to minimize the impact of deconvolved noise at frequencies which have a poor signal-to-noise ratio.

The Wiener deconvolution method has widespread use in image deconvolution applications, as the frequency spectrum of most visual images is fairly well behaved and may be estimated easily.

Wiener deconvolution is named after Norbert Wiener.

Given a system:

where ${\displaystyle *}$ denotes convolution and:

Our goal is to find some ${\displaystyle \ g(t)}$ so that we can estimate ${\displaystyle \ x(t)}$ as follows:

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