Reply to Farina and Enoka: The Reconstruct-and-Test Approach Is the Most Appropriate Validation for Surface EMG Signal Decomposition to Date

reply: We thank Drs. Farina and Enoka for recognizing our surface electromyographic (sEMG) signal decomposition technology as being “impressive” and for appreciating that “the approach is far superior to even the most optimistic expectations in the field.” We will use this opportunity to assuage doubts they and others might have, to correct their misunderstanding, and to expand on the advantages of our accuracy verification approach. They begin by casting doubt on our algorithm's ability to resolve N overlapping action potentials in complex signal segments by relying on the notion that “global optimization of overlapping action potentials is a…NP-hard problem that cannot be solved by polynomial complexity algorithms.” To those not versed in complexity theory, the jargon of NP-hard (nondeterministic polynomial time-hard) can create the mistaken impression that such problems are impossible to solve in any practical way unless N is small (say N 95.2% on average) is an empirical validation that for relatively large values of N, a great preponderance of segments in real sEMG signals can be resolved correctly. They proceed to question the accuracy assessments we reported for our algorithm. They make four claims, each of which shows a major misunderstanding of our reconstruct-and-test approach.