A computer system for detecting neuronal action potential signals from target neural tissue responding to electrical stimulation signals applied by an implant stimulation electrode (no), the system comprising: a response measurement module containing a combination of software and hardware for generating electrical stimulation pulses for the target neural tissue and recording and analyzing the neuronal action potential signals, an external transmitter, and a control interface, wherein said external transmitter is configured for transmitting NAP responses recorded at said implant stimulation electrode through said control interface to said response measurement module, a sparse signal space model for a set of tissue response recordings, the model having a signal model space separable into a plurality of disjoint component manifolds including a neural action potential component manifold corresponding to tissue response to electrical stimulation signals; and said response measurement module configured to: i. map an individual tissue response measurement signal into the signal model space to obtain a corresponding sparse signal representation; ii. project the sparse signal representation onto the NAP component manifold to obtain a sparse NAP component representation; and iii. if the energy in the sparse NAP component representation of the manifold is greater than a minimum threshold value, report a detected NAP signal in the individual tissue response measurement signal. a response measurement module containing a combination of software and hardware for generating electrical stimulation pulses for the target neural tissue and recording and analyzing the neuronal action potential signals, an external transmitter, and a control interface, wherein said external transmitter is configured for transmitting NAP responses recorded at said implant stimulation electrode through said control interface to said response measurement module, a sparse signal space model for a set of tissue response recordings, the model having a signal model space separable into a plurality of disjoint component manifolds including a neural action potential component manifold corresponding to tissue response to electrical stimulation signals; and said response measurement module configured to: i. map an individual tissue response measurement signal into the signal model space to obtain a corresponding sparse signal representation; ii. project the sparse signal representation onto the NAP component manifold to obtain a sparse NAP component representation; and iii. if the energy in the sparse NAP component representation of the manifold is greater than a minimum threshold value, report a detected NAP signal in the individual tissue response measurement signal. i. map an individual tissue response measurement signal into the signal model space to obtain a corresponding sparse signal representation; ii. project the sparse signal representation onto the NAP component manifold to obtain a sparse NAP component representation; and iii. if the energy in the sparse NAP component representation of the manifold is greater than a minimum threshold value, report a detected NAP signal in the individual tissue response measurement signal.