Efficient Sparse Coding in Early Sensory Processing: Lessons from Signal Recovery

Sensory representations are not only sparse, but often overcomplete: coding units significantly outnumber the input units. For models of neural coding this overcompleteness poses a computational challenge for shaping the signal processing channels as well as for using the large and sparse representations in an efficient way. We argue that higher level overcompleteness becomes computationally tractable by imposing sparsity on synaptic activity and we also show that such structural sparsity can be facilitated by statistics based decomposition of the stimuli into typical and atypical parts prior to sparse coding. Typical parts represent large-scale correlations, thus they can be significantly compressed. Atypical parts, on the other hand, represent local features and are the subjects of actual sparse coding. When applied on natural images, our decomposition based sparse coding model can efficiently form overcomplete codes and both center-surround and oriented filters are obtained similar to those observed in the retina and the primary visual cortex, respectively. Therefore we hypothesize that the proposed computational architecture can be seen as a coherent functional model of the first stages of sensory coding in early vision. Author Summary: Neural systems favor overcomplete sparse codes in which the number of potential output neurons may exceed the number of input neurons, but only a small subset of neurons become actually active. We argue that efficient use of such large dimensional overcomplete sparse codes requires structural sparsity by controlling the number of active synapses. Motivated by recent results in signal recovery, we introduce a particular signal decomposition as a pre-filtering stage prior to the actual sparse coding, which efficiently supports structural sparsity. In contrast to most models of sensory processing, we hypothesize that the observed transformations may actually realize parallel encoding of the stimuli into representations that describe typical and atypical parts. When trained on natural images, the resulting system can handle large, overcomplete representations and the learned transformations seem compatible with the various receptive fields characteristic to different stages of early vision. In particular, transformations realized by the prefiltering units can be approximated as ‘Difference-of-Gaussians’ filters, similar to the receptive fields of neurons in the retina and the LGN. In addition, sparse coding units have localized and oriented edge filters like the receptive fields of the simple cells in the primary visual cortex, V1.