Optimal design of 2D digital filters based on neural networks

Abstract

Two-dimensional (2-D) digital filters are widely useful in image processing and other 2-D digital signal processing fields,but designing 2-D filters is much more difficult than designing one-dimensional (1-D) ones.In this paper, a new design approach for designing linear-phase 2-D digital filters is described,which is based on a new neural networks algorithm (NNA).By using the symmetry of the given 2-D magnitude specification,a compact express for the magnitude response of a linear-phase 2-D finite impulse response (FIR) filter is derived.Consequently,the optimal problem of designing linear-phase 2-D FIR digital filters is turned to approximate the desired 2-D magnitude response by using the compact express.To solve the problem,a new NNA is presented based on minimizing the mean-squared error,and the convergence theorem is presented and proved to ensure the designed 2-D filter stable.Three design examples are also given to illustrate the effectiveness of the NNA-based design approach.