Deconvolution

Deconvolution is, in mathematics, the inverse operation of convolution, and it is used in signal processing and image processing to recover an original signal after it has passed through a filter. Given the convolution equation f convolved with g equals h, where h is a recorded, distorted signal, f is the unknown original signal, and g is the filter or distortion function, deconvolution attempts to recover f, either by knowing g in advance or by estimating it statistically or from physical principles of the system. In practice, simply inverting the filter is not always effective, because measurement noise is amplified in the process, so a poor signal to noise ratio significantly degrades how well the original signal can be reconstructed. The theoretical foundations of deconvolution were developed by Norbert Wiener at MIT during the Second World War and published in 1949, with early applications in weather forecasting and economics as well as signal processing.