  Deconvolution is the important problem of estimating the distribution of a
quantity of interest from a sample with additive measurement error. Nearly all
methods in the literature are based on Fourier transformation because it is
mathematically a very neat solution. However, in practice these methods are
unstable, and produce bad estimates when signal-noise ratio or sample size are
low. In this paper, we develop a new deconvolution method based on maximum
likelihood with a smoothness penalty. We show that our new method has much
better performance than existing methods, particularly for small sample size or
signal-noise ratio.
