Discrete-Time Neural Network for Fast Solving Large Linear $L_{1}$ Estimation Problems and its Application to Image Restoration

There is growing interest in solving linear L₁ estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L₁ estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L₁ estimation problems but also needs much less computational time than the related algorithms in solving both linear L₁ estimation and image restoration problems.