A Globally Stable LPNN Model for Sparse Approximation

Hao Wang, Ruibin Feng, Chi-Sing Leung, John Sum, Anthony G. Constantinides

Abstract: The objective of compressive sampling is to determine a sparse vector from an observation vector. This brief describes an analog neural method to achieve the objective. Unlike previous analog neural models which either resort to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> -norm approximation or are with local convergence only, the proposed method avoids any approximation of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> -norm term and is probably capable of leading to the optimum solution. Moreover, its computational complexity is lower than that of the other three comparison analog models. Simulation results show that the error performance of the proposed model is comparable to several state-of-the-art digital algorithms and analog models and that its convergence is faster than that of the comparison analog neural models.