Design of Two-Dimensional Recursive Filters Using Bacteria Foraging Optimization Rutuparna Panda and Manoj Kumar Naik Department of Electronics and Telecommunication Engineering Veer Surendra Sai University of Technology Burla, Odisha -768018 (India) Phone: 91-663-2431857, Fax: 91-663-2430204 E-mail: r_ppanda@yahoo.co.in and naik.manoj.kumar@gmail.com Niranjan Mishra Einstein Academy of Technology and Management Bhubaneswar, Odisha (India) E-mail: mishra_niranjan@rediffmail.com Abstract— This paper presents a method for design of two dimensional (2-D) recursive filters using bacteria foraging optimization (BFO) technique. The design of 2-D recursive filter is considered as a constrained optimization problem. The solution is obtained through the convergence of a biased random search using BFO. With the help of numerical illustrations, we present the theoretical results. Comparison with the results of earlier methods is made. Keywords— Multidimensional systems, two dimensional recursive filters, constrained optimization, Neural Networks, Genetic Algorithm, Bacteria Foraging Optimization. I. INTRODUCTION The last four decades has witnessed various methods for design of two-dimensional (2-D) recursive and non-recursive filters that are useful in biomedical image processing, biomedical imaging, pattern recognition, remote sensing, astronomy, seismic data processing [1, 2] etc. Many authors have proposed design methods for 2-D recursive filters. This has been a worthwhile subject of study. In general, design methods for 2-D recursive filters are classified into two different categories: (i) methods using transformation of one- dimensional (1-D) filters [2]; (ii) methods using various transformation techniques [3-10]. It is important to note here that the stability of the digital filter is very much needed for practical realization. However, most of the existing techniques [3-10] provide us unstable filters. This has been discussed in [11, 12]. The authors in [3- 10] proposed methods for design of 2D recursive filters, which are based on optimization techniques. The stability of filters has not been ensured, because those approaches were based on more or less trial-and-error basis. To overcome this problem, one approach to avoid the instability, design of 2D recursive filters using continuous-time neural network (NN) was proposed in [11]. Later the researchers improved the stability margin using genetic algorithm (GA) [12, 13]. They adopted GA, which uses a purely random search strategy. The offspring never end with a desired location. On the other hand, bacteria foraging optimization (BFO) gives us a random bias walk. In this paper, the proposed BFO algorithm offers us two distinct additional advantages - (i) the proposed algorithm supplements the features of GA, and (ii) the random bias incorporated into the BFO [14] algorithm guides us to move in the direction of increasingly favorable environment. In addition, BFO algorithm allows us for a physical dispersal of the child in a chosen area. Hence, is useful to further reduce the approximation error. This has motivated us to investigate design method for 2-D recursive filters using BFO technique. Authors in [15, 16] have solved the design problem using differential evolution (DE) and particle swarm optimization (PSO) techniques. Here we use BFO to design 2D recursive filters with improved performance. E. coli bacteria foraging optimization (BFO) technique is a new distributed optimization technique introduced in [14]. The proposed algorithm emulates the chemotaxis (foraging) behaviour of E. coli bacteria, which can be used to solve non gradient optimization problems with the help of a run and tumble mechanism to move the cell in right direction. Note that the motion patterns of bacteria are decided using swarming (where cell releases attractants for signalling other cells so they can swarm together) behaviour. There are other important steps in bacterial foraging optimization technique – reproduction, elimination and dispersal. These steps are very important and reflect various activities of social bacterial foraging. In the reproduction step, the least healthy bacteria die as they could not search food with high nutrient value during their lifetime of foraging. However, the healthiest bacteria can reproduce (each split into two). In the elimination-dispersal step, any bacteria can be eliminated from the population by dispersing it to a desired location. The frequency of chemotactic steps in BFO is greater than the frequency of reproduction steps. Characteristics of chemotactic and swarming behaviour of E. coli bacteria are reported in [14]. In this paper, we ignore some characteristics of chemotactic and swarming in order to make our simulation programs simple. The stability of BFO is discussed in [17-18]. BFO is useful for various engineering applications (to solve optimization problems). Recently, the bacteria foraging optimization has been used in [19-21], which outperforms the GA. In this 188 978-1-4673-6004-3/13/$31.00 c 2013 IEEE