Least-squares deconvolution of evoked potentials and sequence optimization for multiple stimuli under low-jitter conditions

Objective: Rapid presentation of stimuli in an evoked response paradigm can lead to overlap of multiple responses and consequently difficulties interpreting waveform morphology. This paper presents a deconvolution method allowing overlapping multiple responses to be disentangled. Methods: The deconvolution technique uses a least-squared error approach. A methodology is proposed to optimize the stimulus sequence associated with the deconvolution technique under low-jitter conditions. It controls the condition number of the matrices involved in recovering the responses. Simulations were performed using the proposed deconvolution technique. Results: Multiple overlapping responses can be recovered perfectly in noiseless conditions. In the presence of noise, the amount of error introduced by the technique can be controlled a priori by the condition number of the matrix associated with the used stimulus sequence. The simulation results indicate the need for a minimum amount of jitter, as well as a sufficient number of overlap combinations to obtain optimum results. An aperiodic model is recommended to improve reconstruction. Conclusions: We propose a deconvolution technique allowing multiple overlapping responses to be extracted and a method of choosing the stimulus sequence optimal for response recovery. Significance: This technique may allow audiologists, psychologists, and electrophysiologists to optimize their experimental designs involving rapidly presented stimuli, and to recover evoked overlapping responses.