Optimal resolution of superimposed action potentials

This paper presents a practical algorithm for resolving superimposed action potentials encountered during the decomposition of electromyographic signals. The problem is posed as an optimization problem: to align a set of templates with a given waveform to minimize the euclidean distance between them. The algorithm uses a recursive approach to search all possible discrete-time alignments, starting with the most likely ones and stopping once it can be verified that the optimal alignment has been found. Each candidate solution is aligned to finer-than-sampling-interval resolution using interpolation and continuous-time optimization. Both the cases in which the identities of the involved templates are known and not known are considered. Simulations are presented to show that the proposed algorithm is very accurate even for complex superpositions involving three or more similarly shaped templates, destructive interference, and added noise.