Ordinary Differential Equation-based Sparse Signal Recovery

In this paper, continuous-time dynamical systems solving sparse signal recovery problems are presented. The proposed dynamical system is expressed by a nonlinear ODE (ordinary differential equation), which is based on the gradient dynamics involving the gradient of the lasso objective function. The effectiveness of the proposed dynamical system is shown by numerical experiments using the Euler method for solving the proposed ODE. Furthermore, we propose a variational optimization problem for tuning a time-dependent regularization parameter to obtain improved convergence. We propose the deep unfolded-variational optimization (DU-VO) method for solving variational optimization problems. The DU-VO method is applied to the ODE-based sparse signal recovery and the numerical results indicate the effectiveness of this approach.