Continuous-Time Sparse Signal Recovery

Abstract

This study investigates a continuous-time method for sparse signal recovery, which is suitable for analog optical circuit implementation. The proposed method is defined by a nonlinear ordinary differential equation (ODE) derived from the gradient flow dynamics of the Lasso objective function. Numerical experiments show that the proposed method certainly finds original sparse vectors within reasonable accuracy. To gain insight into the local convergence properties of the proposed method, a linear approximation around the equilibrium point is applied, yielding a closed-form error evolution ODE. This analysis shows the behavior of convergence to the equilibrium point. In addition, a variational optimization problem is proposed to optimize a time-dependent regularization parameter in order to improve both convergence speed and solution quality. The deep unfolded variational optimization method is introduced as a means of solving this optimization problem, and its effectiveness is validated through numerical experiments.

Keywords

• Optical computing
• analog computing
• optical circuit
• sparse signal recovery
• Lasso
• compressed sensing