Computational algorithms and neural circuitry for compressed sensing in the mammalian main olfactory bulb

A major challenge for many sensory systems is the representation of stimuli that vary along many dimensions. This problem is particularly acute for chemosensory systems because they require sensitivity to a large number of molecular features. Here we use a combination of computational modeling and in vivo electrophysiological data to propose a solution for this problem in the circuitry of the mammalian main olfactory bulb. We model the input to the olfactory bulb as an array of chemical features that, due to the vast size of chemical feature space, is sparsely occupied. We propose that this sparseness enables compression of the chemical feature array by broadly-tuned odorant receptors. Reconstruction of stimuli is then achieved by a supernumerary network of inhibitory granule cells. The main olfactory bulb may therefore implement a compressed sensing algorithm that presents several advantages. First, we demonstrate that a model of synaptic interactions between the granule cells and the mitral cells that constitute the output of the olfactory bulb, can store a highly efficient representation of odors by competitively selecting a sparse basis set of \"expert\" granule cells. Second, we further show that this model network can simultaneously learn separable representations of each component of an odor mixture without exposure to those components in isolation. Third, our model is capable of independent and odor-specific adaptation, which could be used by the olfactory system to perform background subtraction or sensitively compare a sample odor with an internal expectation. This model makes specific predictions about the dynamics of granule cell activity during learning. Using in vivo electrophysiological recordings, we corroborate these predictions in an experimental paradigm that stimulates memorization of odorants.