Comment by xeonmc

Basically leverages convolution theorem[0]: expensive convolutions in direct space becomes simple multiplications in reciprocal space, and vice versa.

Whereever you have a convolution operation on your data, transform them to the conjugate domain to turn it into multiplication.

In other words, work in the domain that is natural to your data.

[0] https://en.wikipedia.org/wiki/Convolution_theorem