Reviews: Inverse Filtering for Hidden Markov Models

The paper addresses recovery of the observation sequence given known posterior state estimates, but unknown observations and/or sensor model and also in an extension, noise-corrupted measurements. There is a nice progression of the problem through IP, LP, and MILP followed by a more careful analytical derivation of the answers in the noise-free case, and a seemingly approximate though empirically effective approach (cf. Honestly, most of the motivations seem to be unrealistic, especially the cyber-physical security setting where one does not observe posteriors, but simply an action based on a presumed argmax w.r.t. The EEG application (while somewhat narrow) seems to be the best motivation, however, the sole example is to compare resconstructed observations to a redundant method of sensing -- is this really a compelling application? Is it actually used in practice?