A Compact Cooperative Recurrent Neural Network for Computing General Constrained $L_1$ Norm Estimators

Recently, cooperative recurrent neural networks for solving three linearly constrained L ₁ estimation problems were developed and applied to linear signal and image models under non-Gaussian noise environments. For wide applications, this paper proposes a compact cooperative recurrent neural network (CRNN) for calculating general constrained L ₁ norm estimators. It is shown that the proposed CRNN converges globally to the constrained L ₁ norm estimator without any condition. The proposed CRNN includes three existing CRNNs as its special cases. Unlike the three existing CRNNs, the proposed CRNN is easily applied and can deal with the nonlinear elliptical sphere constraint. Moreover, when computing the general constrained L ₁ norm estimator, the proposed CRNN has a fast convergence speed due to low computational complexity. Simulation results confirm further the good performance of the proposed CRNN.