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On the selection of the cost function for gradient-based decomposition of surface electromyograms

Recently, gradient Convolution Kernel Compensation method was introduced for blind assessment of sparse pulse sequences (PS) out of their convolutive mixtures. This method employs multichannel recordings, is fully automatic and is minimally biased by assumptions about underlying mixing process. In the first step, the unknown mixing channels (convolution kernels) are compensated, whereas in the second step the gradient algorithm is used to blindly optimize the estimated PSs. This paper discusses the selection of the cost functions for aforementioned gradient-based optimization and provides analytical framework for their mutual comparison. Theoretical derivations are validated on both synthetic signals with random mixing matrices and experimental surface electromyograms from abductor pollicis brevis muscle. The analytical derivations agree very well with the results obtained from numerical simulations and establish theoretical guidelines for developing new gradient-based decomposition methods.