Particle Swarm Optimization with Time-Varying Acceleration Coefficients Based on Cellular Neural Network for Color Image Noise Cancellation

Transcription

1 Particle Swarm Optimization with Time-Varying Acceleration Coefficients Base on Cellular Neural Network for Color Image Noise Cancellation Te-Jen Su Jui-Chuan Cheng Yang-De Sun 3 College of Information Technology Kun Shan University Tainan 7 Taiwan R.O.C. 3 Department of Electronic Engineering National Kaohsiung University of Applie Sciences Kaohsiung 87 Taiwan R.O.C. tejensu@mail.ksu.eu.tw eagle@cc.kuas.eu.tw @cc.kuas.eu.tw Abstract This paper proposes a novel metho for esigning templates of Cellular Neural Network (CNN) for color image noise removal. The control of CNN systems is achieve via Particle Swarm Optimization (PSO) with Time-Varying Acceleration Coefficients (). Base on metho the propose approach can automatically upate the parameters of the templates of CNN to optimize them for iminishing noise interference in pollute image. The emonstrate examples are compare favorably with other available methos which illustrate the better performance of the propose -CNN methoology. Keywors- Cellular Neural Network; Color Image Noise Removal; Particle Swarm Optimization with Time-Varying Acceleration Coefficients I. INTRODUCTION Particle swarm optimization is a population base stochastic optimization technique evelope by Dr. Eberhart an Dr. Kenney in 995 [ 9 ] inspire by social behavior of bir flocking or fish schooling. It is easily implemente in most programming languages an has proven both very effective an quick for a iverse set of optimization problems. However local convergence problem an slow later convergence problem are the two critical shortcomings of PSO that limit its applications [3]. A Particle Swarm Optimization with Time-Varying Acceleration Coefficients () is presente in this paper which allows to effectively overcome the two mentione problems []. A novel class of information processing system calle cellular neural networks was propose by L.O. Chua an L. Yang in 988 [6 7]. CNN is characterize by the parallel computing of simple processing cells locally interconnecte. It has been wiely use for image processing pattern recognition signal processing etc. In recent years the problems of CNN templates esign for image processing have receive consierable attention [4 5]. A new metho that combines the iscrete-time cellular neural network template learning metho with an aaptive particle swarm optimization an applies to gray image noise cancelation was evelope [8]. The approach is able to fin the template values easily without complex mathematic computing processes but also to obtain the balance of convergence spee an convergence accuracy. This work is extene from the previous stuy [8]; we attempt to apply the technique of gray image noise cancellation to color image noise cancellation by separating the color image into three Gray-Scale RGB elements. The rest of this paper is organize as follows: in Section the Particle Swarm Optimization techniques while in Section 3 the Cellular Neural Network is iscusse. In Section 4 the CNN base on template learning for images noise cancellation is presente. Examples are given in Section 5 to emonstrate the propose methoology. Finally conclusion is rawn in Section 6. II. PARTICLE SWARM OPTIMIZATION WITH TIME- VARYING ACCELERATION COEFFICIENTS () In PSO suppose that the search space is D-imensional an then the ith particle is represente as X i = (x i x i x id ). The velocity (rate of the position change) of this particle is enote as V i = (v i v i v id ). The best previous position of the ith particle is represente as P i = (p i p i p id ). In other wors P i involves the best previous position which X i has visite (the best position calle pbest). The inex of the best particle among all the particles in the swarm is efine as the symbol g (calle gbest). The particles are manipulate accoring to the equations an. In its canonical form Particle Swarm Optimization is moele as follows [6-8]: vi ( t ) wvi cran( ) ( pi xi ) cran( ) ( pg xi ) () xi ( t ) xi vi ( t ) () where v i (t+) : velocity of particle i at iteration t+ v i (t) : velocity of particle i at iteration t x i (t+) : position of particle i at iteration t+ x i (t) : position of particle i at iteration t c : cognitive parameter c : social parameter ran() : ranom number uniform istribution U() ran() : ranom number uniform istribution U() : pbest position of particle i p i 9

2 p g w : gbest position of swarm : inertia weight The objective of is to enhance the global search in the early part of the optimization an to encourage the particles to converge towar the global optimum at the en of the search. With a large cognitive parameter an small social parameter at the beginning particles are allowe to move aroun the search space instea of moving towar the population best. However a small cognitive parameter an a large social parameter allow the particles to converge to the global optimum in the latter part of the optimization. Uner this evelopment the cognitive parameter c starts with a high value c max an linearly ecreases to c min. Whereas the social parameter c starts with a low value c min an linearly increases to c max. This moification can be mathematically represente as follows: Tmax t c ( c c )( ) c (3) max min min Tmax Tmax t c ( c c )( ) c (4) min max max T where T max is the maximal number of iterations an t is the current number of iterations. III. CELLULAR NEURAL NETWORK A two-imensional CNN array is consiere in which the cell ynamics are escribe by the following nonlinear orinary ifferential equation with linear an nonlinear terms [3 6]: x () t x ()+ t A( i j; k) l y () t B( i j; k) l u () t ij ij kl kl C( k l) Nr( i j) C( k l) Nr( i j) Dij; kl ( v) Iij C( k l) Nr ( i j) max (5) yij f( xij ) xij xij (6) where v u x y () t u x y () t x () t u () t i M j N kl ij ij ij x ij u ij y ij I ij are the state input output an threshol voltage of the specifie CNN cell respectively. A(ij;k) is calle the feeback cloning template B(ij;k) is calle the feeforwar or input control template D ij;kl are nonlinear terms applie for v ( v is a generalize ifference). The state an output vary in time the input is static (time inepenent) an the CNN is single-layer with nearest neighbor linear. In this paper D ij;kl is the generalize nonlinear term applie to v u kl xij the voltage ifference of either the input or state values. The nonlinear template D is as follows: where are the parameters in the nonlinear template D. K shoul be set very close to this value in an attempt to separate the noise effects an the image structure. IV. CNN BASED ON TEMPLATE LEARNING A igital image is compose of pixels which can be thought of as small ots on the screen an may be represente as m-by-n matrices. MATLAB is a matrix processing language for a wie range of applications. The color image in MATLAB is escribe as a two imensional matrix in uint8 format. In orer to apply the gray image noise cancellation from the precious stuy [8] we separate the color image into RGB elements. These three Gray-Scale images will be blen into a colorful image after finishing noise cancellation processes propose. The process followe to perform noise cancellation is shown in Fig. Input Noise Image D ( v) ( v) e MATLAB (Separation) Element:R Element:G Element:B ( v) v ( ) K v u -CNN -CNN -CNN x Image:R Image:G Image:B MATLAB (Blening) Figure. Block iagram of the image separation an blening (7) Output Image In this case is employe to esign templates of CNN for canceling the noise interference in Gray-Scale images. The templates are esigne as following pattern structures respectively: a a a b b b A a a a B b b b D I K a a a b b b where a a a b b b I K are elements of the swarm in orer to satisfy output saturation effectively we set a = b = b = b = I= x ij ()= u ij (t). The training image is corrupte by the salt an pepper noise shown in Fig.. kl ij (8)

3 (a) Figure. The training images (a) Input image to the CNN (b) Desire output image of CNN. The following equation is use as an objective function (error function); the block iagram is shown in Fig. 3. Error k Pc i) P ( i) i ( (9) where k enotes the total pixel of the picture P c (i) is the value of the ith pixel of the input image an P (i) stans for the pixel of the esire output image. Each resulting image is compare with the esire image which shoul be obtaine in the en. The comparison allows to compute the value of the error function an consequently obtain the best template. Figure 3. Block iagram of the objective function. The process for implementing the base on CNN is shown as Fig. 4. (b) V. EXAMPLES AND RESULTS In this section we present the examples pollute by ifferent percentage of noise ensity interference an using our propose metho -CNN compares with PSO-CNN [5] for gray an color image noise cancellation respectively. A. Examples Consier a LENA Gary-Scale image Fig. 5(a) which is pollute by the salt an pepper noise % % 3% in Fig. 5(b) - Fig. 5() respectively. The parameters of the propose metho -CNN an PSO-CNN are set as inicate in Table an Table respectively. The self-aapting inertia weight w is efine in [7]. TABLE I. PARAMETERS SETTING The number of swarm size The maximum position X max The maximum velocity V max Acceleration coefficient c max.5 Acceleration coefficient c min.5 Acceleration coefficient c max.5 Acceleration coefficient c min.5 Inertia weight W.8 Iterations 5 TABLE II. PSO PARAMETERS SETTING The number of swarm size The maximum position X max The maximum velocity V max Acceleration coefficient c.5 Acceleration coefficient c.5 Inertia weight W.8 Iterations 5 Start Initialize each particle ranom position ranom velocity Next particles Cellular Neural Network Simulator Upate the position an velocity of the particle 5(a) 5(b) If a criterion is met? Yes No Determine the pbest i an gbest Get the optimal templates Stop Figure 4. Flow chart of -CNN. 5(c) 5() Figure 5. (a) Original LENA gray-scale image (b) The contaminate image with % noise (c) The contaminate image with % noise () The contaminate image with 3% noise.

4 Accoring to these parameters the consequences of approximate optimal templates A D an threshol K were foun by the after a few iterations. The contaminate image with % noise: PSO-CNN an -CNN Training PSO A D K Error(pixel) 8 6 The contaminate image with % noise: A D The contaminate image with 3% noise: K Iteration Figure 6. -CNN an PSO-CNN Training for Gray image with % noise A D K PSO-CNN an -CNN Training PSO Similarly accoring to above parameters setting the PSO foun the consequences of approximate optimal templates A D an threshol K as following: The contaminate image with % noise: A D The contaminate image with % noise: A K D K Error(pixel) Iteration Figure 7. -CNN an PSO-CNN Training for Gray image with % noise The contaminate image with 3% noise: A D K The error after a few iterations for -CNN an PSO-CNN are shown in Fig Table 3 shows the PSNR [8] of the image noise cancellation with both cases. Error(pixel) PSO-CNN an -CNN Training PSO Iteration Figure 8. -CNN an PSO-CNN Training for Gray image with 3% noise

5 TABLE III. Salt an Pepper PSNR OF THE GRAY IMAGE (56 56 LENA) NOISE CANCELLATION Contaminate Image - CNN PSO-CNN % Noise B B B % Noise.989 B B B 3% Noise.34 B 9.87 B 6.96 B Using the above templates the output images processing by -CNN an PSO-CNN are shown in Fig. 9(a) - 9(c) an Fig. (a) - (c) respectively. By comparing Fig. 6-8 Table 3 an Fig. 9(a) 9(c) with Fig. (a) (c) respectively our propose metho -CNN coul restrain from noise of the pollute image more effectively than PSO-CNN. Next we apply the same optimal templates foun by PSO- TVAC-CNN to the Color images to prove the better performance. B. Examples In orer to emonstrate that the optimal template has the same performance when processing color images we have performe similar tests with the color version of the Lean image (Fig. (a)). The LENA color image in Fig. (b) - () which is pollute by the salt an pepper noise % % 3% respectively. 9(a) 9(b) (a) (b) 9(c) Figure 9. Results by using -CNN algorithm for the Gary- Scale image with noise of (a) % (b)% (c)3% (a) (b) (c) () Figure. (a) Original LENA color image (b) The contaminate image with % noise (c) The contaminate image with % noise () The contaminate image with 3% noise. By using the propose metho -CNN an meian filter the results for the output images obtaine in Fig. (a) - (c) an 3(a) - 3(c). Table 4 show the PSNR of the color image noise cancellation with both cases. TABLE IV. PSNR OF THE COLOR IMAGE (56 56 LENA) NOISE CANCELLATION Salt an Pepper Contaminate Image -CNN Meian filter (c) Figure. Results by using PSO-CNN algorithm for the Gary-Scale image with noise of (a) % (b)% (c)3% % Noise B B B % Noise.43 B B B 3

6 3% Noise.364 B 8.38 B.937 B coul restrain from noise of the pollute image more effectively than PSO-CNN. (a) (b) VI. CONCLUSION In this paper we have presente a Cellular Neural Network templates learning metho that combine Particle Swarm Optimization with Time-Varying Acceleration Coefficients applie to color image noise cancellation. Template learning is a crucial step in cellular neural network technology. The implementation of -CNN is a contribution to the moern heuristics research in the image processing area. From the emonstrate examples the propose algorithm shows the better performance of the noise cancellation for color image than PSO-CNN. In the future research we hope to improve the aaptive templates training to repair the color images that are pollute by the higher ensity of miscellaneous noises. For real applications the propose metho may be implemente an fabricate on FPGA or VLSI technology. Figure. Results by using -CNN algorithm for the color image with noise of (a) % (b)% (c)3%. 3(a) (c) 3(b) 3(c) Figure 3. Results by using meian filter algorithm for the color image with noise of (a) % (b)% (c)3%. By comparing Fig. (a) - (c) with Fig. 3(a) - 3(c) an Table 4 our propose metho (-CNN) REFERENCES [] J. Kenney an R. C. Eberhart Particle Swarm Optimization Proceeings of IEEE International Conference on Neural Networks Perth Australia pp [] J. Kenney an R. C. Eberhart A New Optimizer Using Particle Swarm Theory Proceeings of the Sixth International Symposium on Micromachine an Human Science Nagoya Japan pp [3] D.X. Zhang Z. Hong Guan X.Z. Liu An aaptive particle swarm optimization algorithm an simulation Proceeings of the IEEE International Conference on Automation an Logistics pp [4] M. Nakagawa T. Inoue an Y. Nishio CNN Template Learning To Obtain Desire Images Using Back Propagation Algorithm IEEE Workshop on Nonlinear Circuit Networks pp [5] T. J. Su T. H. Lin J. an W. Liu Particle Swarm Optimization for Gray-Scale Image Noise Cancellation International Conference on Intelligent Information Hiing an Multimeia Signal Processing pp [6] L. O. Chua an L. Yang Cellular Neural Networks: Theory IEEE Trans. Circuits Syst. vol. 35 pp.57 7 Oct [7] L. O. Chua an L. Yang Cellular Neural Networks: Applications IEEE Trans. Circuits Syst. vol. 35 pp.73 9 Oct [8] T. J. Su J. C. Cheng M. Y. Huang T. H. Lin an C. W. Chen Applications of Cellular Neural Networks to Noise Cancelation in Gray Images Base on Aaptive Particle-swarm Optimization Circ. Syst. Signal Jan. oi:.7/s x. [9] F. Heppner an U. Grenaner: A Stochastic Nonlinear Moel for Coorinate Bir Flocks The Ubiquity of Chaos AAAS Publications Washington DC 99. [] Y. Shi an R. Eberhart A Moifie Particle Optimizer Proceeings of the 998 IEEE Worl Congress on Computational Intelligence pp May 998. [] Y. Shi an R. Eberhart Parameter Selection in Particle Swarm Optimization Proceeings of the 7th International Conference on Evolutionary Programming VII Lecture Notes In Computer Science pp [] A. Ratnaweera Saman K. Halgamuge an Harry C. Watson Self- Organizing Hierarchical Particle Swarm Optimizer with Time- 4

7 Varying Acceleration Coefficients IEEE Transactions on Evolutionary Computation Vol. 8 No. 3 pp [3] P. L. Venetianer T. Roska an L. O. Chua Analogic CNN Algorithms for Some Image Compression Decompression an Restoration Tasks IEEE Transactions on Circuits an Systems I: Funamental Theory an Applications Vol. 4 No. 5 pp [4] A. Zarany F. Werblin T. Roska an L. O. Chua Novel Types of Analogic CNN Algorithms for Recognizing Bank-Notes CNNA-94 Thir IEEE International Workshop on Cellular Neural Networks an their Applications pp Dec [5] A. Zarany A. Stoffels T. Roska an L. O. Chua Implementation of Binary an Gray-Scale Mathematical on the CNN Universal Machine IEEE Transactions on Circuits an Systems I: Funamental Theory an Applications Vol. 45 No. pp [6] C. Rekeczky T. Roska an A. Ushia CNN-Base Difference- Controlle Aaptive Nonlinear Image Filters International Journal of Circuit Theory an Applications Vol. 6 pp [7] M. Zhang C. J Li X.H. Yuan Y.C. Zhang An improve PSO an its application in research on reservoir operation function of longterm Thir International Conference on Natural Computation vol. 4 pp [8] R. Lukac an K. N. Plataniotis A Taxonomy of Color Image Filtering an Enhancement Solutions Avances in Imaging an Electron Physics Vol. 4 pp