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.

翻译：为实现模拟压缩感知，本文研究了$\ell_1$正则化函数与极小极大凹惩罚（MCP）正则化函数的近似邻近算子。具体而言，我们提出利用PN结二极管的正向电压-电流（V-I）特性，通过电子模拟电路实现这些近似函数。为验证所提方法的有效性，我们将所设计的$\ell_1$与MCP正则化函数近似邻近算子应用于基于邻近梯度法的压缩感知中。通过计算机仿真，在考虑模拟器件引入加性噪声影响的前提下，验证了采用所提近似邻近算子的算法在稀疏重构方面的性能表现。