$f:\mathbb{R}^n\rightarrow\mathbb{R}$ 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.