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We investigate the sparse functional identification of complex cells and thedecoding of visual stimuli encoded by an ensemble of complex cells. Thereconstruction algorithm of both temporal and spatio-temporal stimuli isformulated as a rank minimization problem that significantly reduces the numberof sampling measurements (spikes) required for decoding. We also establish theduality between sparse decoding and functional identification, and providealgorithms for identification of low-rank dendritic stimulus processors. Theduality enables us to efficiently evaluate our functional identificationalgorithms by reconstructing novel stimuli in the input space. Finally, wedemonstrate that our identification algorithms substantially outperform thegeneralized quadratic model, the non-linear input model and the widely usedspike-triggered covariance algorithm.

Sparse Functional Identification of Complex Cells from Spike Times and the Decoding of Visual Stimuli