I have a binary 2D image that consists of 95% black pixels with a few white pixels scattered about, and I want to convolve it with a 2D gaussian kernel. I'm hoping to exploit its sparsity to improve the efficiency of the blurring.
For simplicity, lets consider my signal to be 1-dimensional. Since the signal is just a superposition of a relatively small number of shifted Kronecker deltas, is there a shortcut for computing it's discrete Fourier transform?
(Apologies in advance for asking a probably obvious question, I'm a lowly computer scientist, not a math major :-) ).