How do you deconvolve irregularly sampled points? $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a signal and $g:\mathbb{R}^n\rightarrow\mathbb{R}$ is a known point-spread function (say, a Gaussian).

A system samples $f\star g$ at a known sequence of irregular points, $(\mathbf{x}_n)_n$. Are there any methods, analytic or numerical, to deconvolve the samples from $g$ to reveal samples of $f$? 

If $f$ were band-limited and the sequence of sample points $(\mathbf{x}_n)_n$ were periodic and finer than the sampling theorem's frequency, then I believe by the convolution theorem sampled-$g$'s  Fourier transform could be divided out pointwise from that of sampled-$f\ast g$, yielding sampled-$f$'s Fourier transform.
You can use a graph-based Signal Processing framework to apply regular deconvolution algorithms. The whole point is that traditional operators (such as FFT) can be defined on graph structures, and graph structures do handle "by design" without any overhead irregular sampling patterns.

Some useful reference scan be found on my former office mate's webpage.