Two-Dimensional IIR Filter Design Using Simulated Annealing Based Particle Swarm Optimization

We present a novel hybrid algorithm based on particle swarm optimization (PSO) and simulated annealing (SA) for the design of two-dimensional recursive digital filters. The proposed method, known as SA-PSO, integrates the global search ability of PSO with the local search ability of SA and offsets the weakness of each other. The acceptance criterion of Metropolis is included in the basic algorithm of PSO to increase the swarm’s diversity by accepting sometimes weaker solutions also. The experimental results reveal that the performance of the optimal filter designed by the proposed SA-PSO method is improved. Further, the convergence behavior as well as optimization accuracy of proposed method has been improved significantly and computational time is also reduced. In addition, the proposed SA-PSO method also produces the best optimal solution with lower mean and variance which indicates that the algorithm can be used more efficiently in realizing two-dimensional digital filters. 1. Introduction Design of two-dimensional (2D) filters has been considered extensively over the past two decades as it plays a very significant role in the domain of biomedical image processing, satellite imaging, seismic data processing, and so forth [1]. It is well known that digital filters are typically classified into two groups: recursive or infinite impulse response (IIR) and nonrecursive or finite impulse response (FIR) filters. Design of IIR filters has received much more attention, because IIR filters can provide a better performance than FIR filters, having the same number of filter coefficients. But the main problems of IIR filters are that they have a multimodal error surface and they may also be unstable in some cases. To overcome the problem of multimodal error surface, a global optimization method can be adopted more efficiently. The stability problem can be tackled by limiting the problem space as appropriate constraints from the beginning of optimization routine [1, 2]. Similar to 1D filter, 2D IIR filters can also meet the same desired specifications with less number of coefficients than required for an equivalent 2D FIR filter. The design methodology for 2D filters grouped in two ways: McClellan transformation based design of 2D filters from 1D prototype and another one based on appropriate optimization techniques [1–6]. In optimization based methods, the design problem can be formulated as a constrained minimization problem and they are solved by various global optimization techniques. Previously reported work on this problem has applied different optimization