A New Approach to Model Pitch Perception Using Sparse Coding

Our acoustical environment abounds with repetitive sounds, some of which are related to pitch perception. It is still unknown how the auditory system, in processing these sounds, relates a physical stimulus and its percept. Since, in mammals, all auditory stimuli are conveyed into the nervous system through the auditory nerve (AN) fibers, a model should explain the perception of pitch as a function of this particular input. However, pitch perception is invariant to certain features of the physical stimulus. For example, a missing fundamental stimulus with resolved or unresolved harmonics, or a low and high-level amplitude stimulus with the same spectral content–these all give rise to the same percept of pitch. In contrast, the AN representations for these different stimuli are not invariant to these effects. In fact, due to saturation and non-linearity of both cochlear and inner hair cells responses, these differences are enhanced by the AN fibers. Thus there is a difficulty in explaining how pitch percept arises from the activity of the AN fibers. We introduce a novel approach for extracting pitch cues from the AN population activity for a given arbitrary stimulus. The method is based on a technique known as sparse coding (SC). It is the representation of pitch cues by a few spatiotemporal atoms (templates) from among a large set of possible ones (a dictionary). The amount of activity of each atom is represented by a non-zero coefficient, analogous to an active neuron. Such a technique has been successfully applied to other modalities, particularly vision. The model is composed of a cochlear model, an SC processing unit, and a harmonic sieve. We show that the model copes with different pitch phenomena: extracting resolved and non-resolved harmonics, missing fundamental pitches, stimuli with both high and low amplitudes, iterated rippled noises, and recorded musical instruments.
Author Summary By means of a sound's pitch, we can easily discern between low and high musical notes, regardless of whether they originate from a guitar, piano or a vocalist. The relation between different sounds that yield the same percept is what makes pitch an interesting subject of research. Today, despite extensive research, the mechanism behind this physical to perceptual transformation is still unclear. The large dynamic range of the cochlea combined with its nonlinear nature makes the modeling and understanding of this process a challenging task. Given a large amount of physiological and psychological data, a general explanation consistent with many of these phenomena would be a major step in elucidating the nature of pitch perception. In this paper, we recast the problem in the general framework of sparse coding of sensory stimuli. This framework, initially developed for the visual modality, posits that the goal of the neural representation is to represent the flow of sensory information in a concise and parsimonious way. We show that applying this principle to the problem of pitch perception can explain many perceptual phenomena.