Weighted 2D convolution

Hi, I wish to perform a weighted 2D convolution, or more precisely summing a kernel zone by zone, but given a different weighing for each zone. For example, let's say I have an image of 100x100 pixels, and wish to sum the contribution of 16 Gaussians with centers spread equally within the image, with a kernel of size 20x20 pixels, but each has a different weight (random between 50 and 100%). Could anyone hint me which functions to use, examples? Thanks.