Nonlinear RNN with noise-immune: A robust and learning-free method for hyperspectral image target detection

While the recurrent neural network (RNN) has achieved remarkable performance on dynamic and control tasks, its applications to image processing, particularly target detection are limited. Challenges arise from differences between the two domains, such as the way for merging time information into static problems and variances of dynamic and static solving methods. To this end, we first extend the existing constrained energy minimization (CEM)-based detection scheme to a dynamic version, e.g. dynamic reinforced CEM (DRCEM), which injects the dynamic information. After that, aided by the rigorous mathematical derivation and optimization theory, the DRCEM is merged into the RNN solution framework. To enhance the robustness and convergence of the existing RNN solutions for improving DRCEM performance, the nonlinear and bounded-constraint RNN (NBCRNN) is designed by developing a novel nonlinear activation function, then applying the proposed model to implement the DRCEM scheme. The corresponding theorem results reveal the proposed model possesses global convergence and enhanced robustness. Compared to state-of-the-art works, the DRCEM solved by the NBCRNN model detection method achieves better detection accuracy, with 1.82% improvement in terms of the Kappa coefficient, and reduces the residual error from 10−4 to 10−7. Furthermore, our detection method is able to preserve the detection accuracy in presence of noise perturbated. To the best of our knowledge, it is the first work to develop the zeroing-type RNN for hyperspectral image target detection. The code and models are publicly available at Github DRCEM_NBCRNN Code Implementation.