Robust Regression Estimation Based on Low-Dimensional Recurrent Neural Networks

The robust Huber's M-estimator is widely used in signal and image processing, classification, and regression. From an optimization point of view, Huber's M-estimation problem is often formulated as a large-sized quadratic programming (QP) problem in view of its nonsmooth cost function. This paper presents a generalized regression estimator which minimizes a reduced-sized QP problem. The generalized regression estimator may be viewed as a significant generalization of several robust regression estimators including Huber's M-estimator. The performance of the generalized regression estimator is analyzed in terms of robustness and approximation accuracy. Furthermore, two low-dimensional recurrent neural networks (RNNs) are introduced for robust estimation. The two RNNs have low model complexity and enhanced computational efficiency. Finally, the experimental results of two examples and an application to image restoration are presented to substantiate superior performance of the proposed method over conventional algorithms for robust regression estimation in terms of approximation accuracy and convergence rate.