Sparse coding with a global connectivity constraint

Basis pursuit via sparse coding techniques have generally enforced sparseness by using L1-type norms on the coefficients of the bases. When applied to natural scenes these algorithms famously retrieve the Gabor-like basis functions of the primary visual cortex (V1) of the mammalian brain. In this paper, inspired further by the architecture of the brain, we propose a technique that not only retrieves the Gabor basis but does so respecting global power-law type connectivity patterns. Such global constraints are beneficial from a biological perspective in terms of efficient wiring, robustness etc. We draw on the similarity between sparse coding and neural networks to formulate the problem and impose such global connectivity patterns.