  Computing sparse redundant representations is an important problem both in
applied mathematics and neuroscience. In many applications, this problem must
be solved in an energy efficient way. Here, we propose a hybrid distributed
algorithm (HDA), which solves this problem on a network of simple nodes
communicating via low-bandwidth channels. HDA nodes perform both
gradient-descent-like steps on analog internal variables and
coordinate-descent-like steps via quantized external variables communicated to
each other. Interestingly, such operation is equivalent to a network of
integrate-and-fire neurons, suggesting that HDA may serve as a model of neural
computation. We show that the numerical performance of HDA is on par with
existing algorithms. In the asymptotic regime the representation error of HDA
decays with time, t, as 1/t. HDA is stable against time-varying noise,
specifically, the representation error decays as 1/sqrt(t) for Gaussian white
noise.
