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

TL;DR

This work targets analog compressed sensing by designing approximate proximal operators for $J_{\ell1}$ and $J_{\text{MCP}}$ using PN-junction diode forward $V$–$I$ characteristics. The authors derive circuit-based mappings $V_{out}(I_{in})$ that emulate the soft-thresholding and MCP proximal operators, parameterized by resistances $R$ and $R'$, and validate these approximations by integrating them into ISTA and performing simulations that include realistic circuit noise modeled from OEM and EOM components. Results show that diode-$\ell1$ can surpass the ideal soft-thresholding in steady-state MSE, while diode-MCP offers competitive performance with negligible degradation due to circuit noise, illustrating the practical potential of analog implementations. The findings suggest feasible, low-noise analog CS with diode-based proximal operators and motivate further studies on parameter sensitivity and other analog impairments.

Abstract

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.

Figures (6)

• Figure 1: V-I characteristics of PN-junction diode
• Figure 2: Proposed electrical analog circuit using PN-junction diodes to approximate proximal operators.
• Figure 3: Examples of $V_{\mathrm{out}}(I_{\mathrm{in}})$ to approximate soft-thresholding function $\text{prox}_{0.0225 J_{\ell_1}}(I_{\mathrm{in}})$.
• Figure 4: Schematic illustration of proposed approximate proximal operator of MCP regularization function.
• Figure 5: Examples of $V_{\mathrm{out}}(I_{\mathrm{in}})$ to approximate proximal operator $\text{prox}_{0.0225 J_\text{MCP}}(I_{\mathrm{in}})$ for $0 \leq I_{\mathrm{in}} \leq 2$ with $k=1.5$.