In the context of image processing a deconvolution is the inverse of a convolution f = g * h (+ n), i.e. to determine the unknown function g given h and f, while n represents the nosie. One could try to approach this problem with the Fourier transform, as this would yield G = F / H - N / H . However, this will usually enhance the noise term, as the spectrum of the filter H usually flattens for high frequencies, while the noise term still has a lot of power in these frequencies.
There are some other techniques like Wiener deconvolution 111 to counter these noise problems.
Let me know, if I understood your use case right or am completely missing the discussion.