Generally, a convolution in spatial (or time) domain can be turned into a multiplication in the frequency domain. Multiplication is an easier operation to do by hand than convolution, but I think it might actually be faster to do a convolution using a computer than it would be to have to deal with Fourier transforms. That is, I think the amount of work done by converting to the frequency domain doesn't provide enough benefit to justify doing so compared to the computational power needed just to convolve
yykkcc
I Googled that Convolutional Neural Networks (CNNs) can be trained to understand the content of the image and reduce noise, is the 'convolution' here the same idea as that?
henrykhaung
So convolution theorem is just a faster way of convolving two signals by multiplying their representations in another domain. So for example, if you have two signals and say you want to add them, you can just multiply them in the frequency domain to get the same result as adding them in the spatial domain. This way would be faster.
Generally, a convolution in spatial (or time) domain can be turned into a multiplication in the frequency domain. Multiplication is an easier operation to do by hand than convolution, but I think it might actually be faster to do a convolution using a computer than it would be to have to deal with Fourier transforms. That is, I think the amount of work done by converting to the frequency domain doesn't provide enough benefit to justify doing so compared to the computational power needed just to convolve
I Googled that Convolutional Neural Networks (CNNs) can be trained to understand the content of the image and reduce noise, is the 'convolution' here the same idea as that?
So convolution theorem is just a faster way of convolving two signals by multiplying their representations in another domain. So for example, if you have two signals and say you want to add them, you can just multiply them in the frequency domain to get the same result as adding them in the spatial domain. This way would be faster.