Approximate Proximal Operators for Analog Compressed Sensing Using PN-junction Diode

In order to realize analog compressed sensing, the paper considers approximate proximal operators of the $\ell_1$ and minimax concave penalty (MCP) regularization functions. Specifically, we propose to realize the approximate functions by an electric analog circuit using forward voltage-current (V-I) characteristics of the PN-junction diodes. To confirm the validity of the proposed approach, we employ the proposed approximate proximal operators for the $\ell_1$ and MCP regularization functions in compressed sensing with the proximal gradient method. The sparse reconstruction performance of the algorithms using the proposed approximate proximal operators is demonstrated via computer simulations taking into account the impact of additive noise introduced by analog devices.