  Compared with digital methods, sparse recovery based on spiking neural
networks has great advantages like high computational efficiency and low
power-consumption. However, current spiking algorithms cannot guarantee more
accurate estimates since they are usually designed to solve the classical
optimization with convex penalties, especially the $\ell_{1}$-norm. In fact,
convex penalties are observed to underestimate the true solution in practice,
while non-convex ones can avoid the underestimation. Inspired by this, we
propose an adaptive version of spiking sparse recovery algorithm to solve the
non-convex regularized optimization, and provide an analysis on its global
asymptotic convergence. Through experiments, the accuracy is greatly improved
under different adaptive ways.
