An investigation of two-dimensional parameter-induced stochastic resonance and applications in nonlinear image processing

This paper aims at developing an elementary theory of two-dimensional (2D) parameter-induced stochastic resonance (PSR) to contribute to nonlinear image processing. In order to tackle the application of SR in image processing, where adding noise may not be an easy task, we propose to generalize the concept of PSR from the one-dimensional (1D) case to the 2D case. An interesting feature of this paper is that a rigorous analytical framework is developed based on the Fokker–Planck equation (FPE). Some applications to image processing are performed to demonstrate the effectiveness of the approaches based on the proposed theory of 2D PSR. It is believed that the PSR-based methodology as advocated in this paper provides a different, but promising perspective for applying SR techniques to nonlinear image processing.