Deconvolution

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, deconvolution is the <a href="/facts/Inverse_function/Tg5nnXlu">inverse</a> of <a href="/facts/Convolution/PVPrdz9J">convolution</a>. Both operations are used in <a href="/facts/Signal_processing/Npaja6zb">signal processing</a> and <a href="/facts/Image_processing/zenalNCf">image processing</a>. For example, it may be possible to recover the original signal after a filter (convolution) by using a deconvolution method with a certain degree of accuracy. Due to the measurement error of the recorded signal or image, it can be demonstrated that the worse the <a href="/facts/Signal-to-noise_ratio/qohClhyG">signal-to-noise ratio</a> (SNR), the worse the reversing of a filter will be; hence, inverting a filter is not always a good solution as the error amplifies. Deconvolution offers a solution to this problem.
The foundations for deconvolution and <a href="/facts/Time-series_analysis/fSXPR817">time-series analysis</a> were largely laid by <a href="/facts/Norbert_Wiener/cVMRAHCU">Norbert Wiener</a> of the <a href="/facts/Massachusetts_Institute_of_Technology/Xk49vNA8">Massachusetts Institute of Technology</a> in his book Extrapolation, Interpolation, and Smoothing of Stationary Time Series (1949). The book was based on work Wiener had done during <a href="/facts/World_War_II/2efV5L1U">World War II</a> but that had been classified at the time. Some of the early attempts to apply these theories were in the fields of <a href="/facts/Weather_forecasting/nzqyMFCa">weather forecasting</a> and <a href="/facts/Economics/HYctA2Dn">economics</a>.

Deconvolution open-in-new

Deconvolution