Inverse convolution

1. What is the inverse of convolution?
2. Can we invert convolution?
3. What is the purpose of deconvolution?
4. What is convolution in FFT?

What is the inverse of convolution?

Computing the inverse of the convolution operation is known as deconvolution.

Can we invert convolution?

In the continuous-time case in particular, the convolution may be invertible as long as the zeros are isolated.

What is the purpose of deconvolution?

Deconvolution is a computational method that treats the image as an estimate of the true specimen intensity and using an expression for the point spread function performs the mathematical inverse of the imaging process to obtain an improved estimate of the image intensity.

What is convolution in FFT?

FFT convolution uses the principle that multiplication in the frequency domain corresponds to convolution in the time domain. The input signal is transformed into the frequency domain using the DFT, multiplied by the frequency response of the filter, and then transformed back into the time domain using the Inverse DFT.