Circuit Design and Analysis of Smoothed l0 Norm Approximation for Sparse Signal Reconstruction

L-0 norm plays a crucial role in sparse optimization, but discontinuities and nonconvexity make the minimization of the l(0) norm be an NP-hard problem. To alleviate this problem, we design a smoothing function based on the sigmoid function to approximate the l(0) norm. To illustrate the physical realizability of the smoothing function and the advanced quality of the approximation, the proposed smoothing function is compared experimentally with several existing smoothing functions. Additionally, we analyze the parameters in the functions to determine the quality of the approximation. We investigate the circuit implementation of the proposed function and five existing smoothing functions; the simulation results show the effectiveness of the designed circuit on the Multisim platform. Experiments on the reconstruction of simulated sparse signals and real image data show that the proposed smoothing function is able to reconstruct sparse signals and images with lower mean square error (MSE) and higher peak signal-to-noise ratio (PSNR), respectively.