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.

翻译：进化是估算从具有添加度误差的样本中获取的一定数量的利息分配的重要问题。文献中几乎所有方法都基于Fourier转换法,因为它在数学上是一个非常整洁的解决办法。然而,在实践上,这些方法不稳定,当信号-噪音比率或样本大小低时,就会产生坏估计。在本文中,我们开发了一种新的分解法,其依据是最有可能的顺畅性罚款。我们发现,我们的新方法比现有方法效果要好得多,特别是对于小样本大小或信号-噪音比率而言。