What does the visual representation of matched filtering of images look like? So I am using the Source Extractor to find point sources in my images and it offers the possibility to use matched filtering to enhance the detection results. In the documentation they also claim that the matched filter defaults to a convolution of the data, should the noise be equal across the field (please correct me if I got this wrong). While there is a nice and easy to understand visual reprentation for the convolution, where the convoluted pixel value is simply the sum of the pixel values &quot;below&quot; the kernel weighted by the factors in the kernel &quot;above&quot;, I have yet to find a similar explanation for what is going on in matched filtering.
I also like how the matched filter is derived in terms of matrices, since I feel like this makes the most sense with image processing (unlike the derivation using itegrals I found in many places), but I haven't found a book yet where this is well explained. Can someone point me to a source where matched filtering is explained regarding image processing?
There's really nothing special about image processing here: the matched filter is still the hermetian, spatially-inverse filter (=convolution kernel) to the original filter (=convolution kernel).
Since images tend to be real-valued, most convolutional kernels are, too. In which case you just flip the kernel along both axes and are done.
If the original kernel is symmetrical along both axes, it's its own matched filter.
The explanations used for the one-dimensional matched filter are the same as for the 2D case:
Cauchy-Schwarz inequality says that, for any given filter energy, a filter that fulfills the above criteria leads to the highest SNR in the additive uncorrelated noise case.