A discrete-time learning algorithm for image restoration using a novel L2-norm noise constrained estimation

This paper proposes a discrete-time learning algorithm for fast image restoration using a novel L2-norm noise constrained estimation. The noise constrained estimation approach can relax the need of the optimal regularization parameter to be estimated. Performance analysis shows that the proposed algorithm can converge globally to a robust optimal weight vector. Compared with the cooperative neural fusion (CNF) algorithm minimizing L1-norm estimation, the proposed algorithm only needs O(N  ) multiplication operationper iteration, instead of O(N2)O(N2) multiplication operation required by the CNF algorithm. Moreover, the proposed fusion approach overcomes the difficulty of estimating the noise error set in the CNF approach. Simulation results show by comparison that under the non-optimal regularization parameter, the proposed algorithm can obtain a better restored estimate in Gaussian mixture noise and can run much faster compared to the CNF algorithm.