UnGauss

Supposing you had some initial point source locations, perhaps at the integers, and a standard deviation of a gaussian effect, you can undo the gaussian effect like so:

Set x(i)'s equal to the point source locations, and t^2 equal to the gaussian effect standard deviation...

Now setting this sum evaluated at each x(i) equal to the final intensity at xi gives a system of n linear equations in n unknowns that can be solved...
For example this could be the final distribution after a gaussian effect with a standard deviation of 1:
It has values .2, .25, .2 at x(i) = 1,2,3

The solve command will look like:

Plugging these coefficients into the equation and setting the standard deviation to a lesser value undoes the Gaussian effect, here I've stepped it back to t=.2:

The lower t is set the sharper the peaks...