why use a convolution filter
Convolution with a Gaussian kernel (filter) guarantees a non-negative result, so such function maps non-negative values to other non-negative values (f:R+âR+). The result is therefore always another valid image. In general, frequency rejection in Image processing in not as crucial as in 1D signals.
Gaussian filters are used in image processing because they have a property that their support in the time domain, is equal to their support in the frequency domain. This comes about from the Gaussian being its own Fourier Transform.