A direct, interval-based method for reconstructing stimuli from noise-robust tuning curves

We present a method for reconstructing stimuli from a tuning curve, completing a tuning curve estimation method published earlier. Stimuli are reconstructed by dividing the stimulus space into intervals and providing boundaries for the probabilities with which they contain a given stimulus. The endpoints of these intervals are calculated as zeros of polynomials of high degree using the efficient direct method of Dixon polynomial resultants. Repeated measurements refine the decomposition, allowing for more accurate statements about the associated probabilities. Our method employs no special assumptions about the noise distribution, removing tractability problems of Bayesian or Maximum Likelihood estimation.