Analysis and Application of a Discrete-Time Neurodynamic Approach for Fast Constrained l₁-Norm Minimization

Discrete-time neurodynamic approaches (also called recurrent neural networks (RNNs)) are easily implemented on software and simulated on digital circuits. First, this paper proposes two modified discrete-time RNNs for quickly dealing with constrained l₁-norm minimization problems. Next, the two modified discrete-time RNNs are proven to be globally convergent to an optimal solution under a large step size. Finally, we apply the obtained results for image recovery. Two convergent discrete-time RNN based algorithms for non-blind image restoration are presented. Due to having a low complexity, the two discrete-time RNNs are more computationally efficient than the existing discrete-time RNN for image restoration. Computed results with application examples show that the two discrete-time RNN-based algorithms are indeed superior to the existing discrete-time RNNbased algorithms with regards to computation time.