Deconvolution is a process that undoes the effects of convolution. It is usually used to restore a signal from a known convolution with a known response.
For example, if the original signal is
and the response is
then their linear convolution is
If we only know g and y and want to restore f, a deconvolution can be used.
After computation, we have
Deconvolution is either linear or circular. To restore the original signal correctly, the deconvolution should be of the same type as the convolution that originally produced the input signal.
Notes: There is no guarantee that deconvolution can always recover the original dataset in practice, as deconvolution is very sensitive to noise and is not very robust. Additionally, if the convolution is performed with the response wrapped, deconvoluting the input signal with the same response will not necessarily restore the original data, even when Wrap Response option is checked in the deconvolution dialog.
To use deconvolution:
Topics covered in this section: