Performing a Deconvolution
en.wikipedia.org/wiki/Wiener_filter

what you are looking for is a Weiner  filter  that takes into account the standard deviations of your data. See http://www.astroml.org/book_figures/chapter10/fig_wiener_filter.html 
 and the description in Wikipedia  for implementation.  Basically you will do what you were suggesting,  but with an additional term in the denominator of the ratio of fft's  that is the fft  of the noise.