Deconvolution and Classification

In a series of papers on Lidar data, magically good classification rates are claimed once data are deconvolved and a dimension reduction technique applied. The latter can certainly be useful, but it is not clear a priori that deconvolution is a good idea in this context. After all, deconvolution adds noise, and added noise leads to lower classification accuracy. I will give a more or less formal argument that in a closely related class of deconvolution problems, what statisticians call "Measurement Error Models", deconvolution typically leads to increased classification error rates. An empirical example in a more classical deconvolution context illustrates the results, and new methods and results relevant to the Lidar data will be discussed.