Estimating Convolution Kernel from Input and Output Images

1. How do you calculate convolution kernel?
2. How do you convolve a kernel with an image?
3. What can we detect if we do convolution over an image?

How do you calculate convolution kernel?

Take Fourier Transform of both original image and blurred image, then divide Fourier transform of blurred image by Fourier transform of original image. This will give you the Fourier transform of kernel (except at frequencies with zero value which lead to division by zero).

How do you convolve a kernel with an image?

Convolution is the process of adding each element of the image to its local neighbors, weighted by the kernel. This is related to a form of mathematical convolution. The matrix operation being performed—convolution—is not traditional matrix multiplication, despite being similarly denoted by *.

What can we detect if we do convolution over an image?

Convolution can achieve something, that the previous two methods of manipulating images can't achieve. Those include the blurring, sharpening, edge detection, noise reduction e.t.c.