Deconvolution of Synthetic 1D Signals - How To?
You cant't recover the original signal through deconvolution. 

A Gaussian kernel is in essence a lowpass filter, i.e. it will remove information at higher frequencies from the signal. Once it's gone, it's gone and you can't recover it.

This problem shows up as "divide by zero" or "divide by a very small number", which then amplifies numerically noise of the original convolution to a massive amount. 

In order to recover the original signal the system must have "sufficient signal to noise ratio in the bandwidth of interest". What exactly that is, depends heavily on your specific application. 

You can de-convolve from a low-shelf or high-shelf filter, but not from a low-pass or anything with a stop band or lots of attenuation at specific frequencies.

You'd also lose some information at the beginning and end of the signal.