CHAPTER 6 COUNTER PROPAGATION NEURAL NETWORK FOR IMAGE RESTORATION

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1 135 CHAPTER 6 COUNTER PROPAGATION NEURAL NETWORK FOR IMAGE RESTORATION 6.1 INTRODUCTION Neural networks have high fault tolerance and potential for adaptive training. A Full Counter Propagation Neural Network (Full CPNN) is used for restoration of degraded images. The quality of the restored imaged image is almost the same as that of the original image. This chapter is organized as follows. In section 6.1, the features of CPN are discussed. In section 6.2, the architecture of Full CPNN is presented. In section 6.3, the training phase of Full CPNN is discussed. Some experimental results which confirm the performance of CPNN for image restoration are presented in section 6.4. Finally section 6.5 concludes the chapter. 6.2 COUNTER PROPAGATION NETWORK Counter Propagation Networks (CPN) are multilayer networks based on a combination of input, competitive and output layer. Counter propagation is a combination of two well-known algorithms: self organizing map of Kohenen and the Grossberg outstar (Liang et al 2002). The Counter Propagation network can be applied in a data compression approximation functions or pattern association.

2 136 Counter propagation networks training include two stages: 1. Input vectors are clustered. Clusters are formed using dot product metric or Euclidean norm metrics. 2. Weights from cluster units to outputs units are made to produce the desired response CPN is classified in two types. They are i) Full counter propagation network and ii) Forward only counter propagation network. CPN advantages are that, it is simple and forms a good statistical model of its input vector environment. The CPN trains rapidly. If appropriately applied, it can save large amount of computing time. It is also useful for rapid prototyping of systems Full Counter Propagation Neural Network (Full CPNN) The full CPNN possess the generalization capability which allows it to produce a correct output even when it is given an input vector that is partially incomplete or partially correct (Freeman and Skapura 1999). Full CPNN can represent large number of vector pairs, x:y by constructing a look up table. Figure 6.1 shows the schematic block diagram of restoration process using full CPNN. The architecture of full CPNN for image restoration is shown in Figure 6.2. The architecture of a counter propagation network resembles an instar and outstar model. Basically, it has two input layers and two output layers with hidden (cluster) layer common to the input and output layers. The model which connects the input layers to the hidden layers is called Instar model and the model which connects the hidden layer to the output layer is called Outstar model. The weights are updated both in the Instar and Outstar model. The Instar model performs the first training and the

3 137 Outstar model performs the second phase of training. The network is a fully interconnected network. The major aim of full CPNN is to provide an efficient means of representing a large number of vector pairs, X:Y by adaptively constructing a look up table. It produces an approximation X:Y based on input of a X vector alone or input of a Y vector alone or input of a X:Y pair, possibly with some distorted or missing elements in either or both the vectors. During the first phase of training of full Counter propagation network, the training pairs X:Y are used to form the clusters. The Full CPNN is used for bi-directional mapping. X is the input image and Y is the degraded image. X* and Y* are the restored and the degraded images respectively. Original image Full Counter- Propagation Neural Network Restored image Degraded image Figure 6.1 The schematic block diagram of the Full CPNN

4 138 Original image Restored image x 1 x 2 W Z 1 V x * 1 x * 2 Z 2 x * n x n Input Layer y 1... Output Layer y * 1 y 2 Z nn y * 2 y m U y * m Neuron Degraded image Degraded image Y* T Figure 6.2 The Architecture of the Full CPNN for image restoration 6.3 TRAINING PHASES OF FULL CPNN The full CPNN is achieved in two phases First Phase This phase of training is called Instar modeled training. The active units are the units in the x- input, z- competitive and y-output layers. In CPNN, the winning unit is allowed to learn. This winning unit uses Kohenen learning rule for its weight updation. This rule is given by

5 139 W ij (k+1) = [1- (k)] w ij (k) + (k) x i= (6.1) U ij (k+1) = [1- (k)] u ij (k) + (k) y j (6.2) Second phase In this phase, only the J unit remain active in the cluster layer. The weights from the winning cluster unit J to the output units are adjusted, so that vector of activation units in the y output layer, y*, is approximation of input vector y; and x* is an approximation of input vector x. This phase is called outstar modelled training. The weight updation is done by the Grossberg learing rule which is used only for outstar learning. In outstar learning, no competition is assumed among the units and the learning occurs for all units in a particular layer. The weight updation rule is given as: V ij (k+1) = V ij (k) + (k) [x i -v ij (k)] (6.3) T ij (k+1) = t ij (k) + (k) [y j -t ij (k)] (6.4) Training Algorithm The algorithm for the Full CPNN network is given below: Step 1: Set X input layer activations to vector X, which is the input image pixels of size n. Set Y input layer activations to vector Y, which is the degraded image pixels of size m.

6 140 Express the input X and output Y as vectors X= { x 1, x 2, x 3 x n } Y= {y 1, y 2, y m } T(n,nn). Step 2: Initialize the weights U(n,nn), W(n,nn), V(n,nn) and Step 3: Find the total input of the i th neuron. n 2 m 2 (6.5) Z x w y u j i i,j k k,j i 1 k 1 minimum values. Find min Z j and thus the winning neuron J, which receives the Step 4: If the number of iterations is greater than the specified number of iterations then stop. Update weights of the winning neuron as given below and then go to step 3. W ij (k+1) = [1- (k)] w ij (k) + (k) x i U ij (k+1) = [1- (k)] u ij (k) + (k) y j V ij (k+1) = V ij (k) + (k) [x i -v ij (k)] T ij (k+1) = t ij (k) + (k) [y j -t ij (k)] where Kohonen learning function (k) = (0) exp k k 0 (6.6)

7 141 (0) is the initial learning rate, k is the number of iterations and k 0 is a positive constant. Similarly, the Grossberg learning function of the output stage (k) = (0) exp k k 0 (6.7) where (0) is the initial learning rate and k 0 is a positive constant. Restoration Procedure Step 1: Give any degraded image as the input X X = {0} Y = {y 1,y 2, y n } Step 2: Find Z j Z j = n 2 (xi w ij) (6.8) i 1 Find min Z j and the winning neuron J. Step 3: Find X* and Y*. X* is the restored image. x * i n v (6.9) i 1 Ji y * j m t (6.10) k 1 Jk

8 EXPERIMENTAL RESULTS The CPNN approach to restore the image is implemented successfully in VC++ and experiments are carried out to evaluate its performance. In the simulation environment where the original signal is available, the improvement in performance is measured using difference in signal to noise ratio between the original image and the restored image. To evaluate the performances of the proposed approach, different experiments are conducted using Lena, mandrill, flowers and boat images of size The quality of restored images has been assessed by Peak Signal- To-Noise Ratio (PSNR). The restored images obtained with this approach are of good visual quality with higher PSNR. Different experiments are conducted with varying values of α and β and quality of the restored image is noted. From the experimental results, it is found that the noisy images are restored to good quality images when the value of α is kept close to 0.7 and β = 0.5. Also, as the value of α is decreased below 0.6 and β value decreased below 0.5, it is found that the restored image quality is very much deteriorated and the mean squared error is high as Figure 6.3 shows a degraded Lena image. Figure 6.4 is the restored Lena image after 25 iterations. PSNR = 49 db Figure 6.3 Degraded Lena image with impulse noise Figure 6.4 Restored Lena image

9 143 A few experiments were also conducted by varying the number of hidden layer neurons and it was found that the quality of the restored image produced is optimum when the number of neurons in the hidden layer is 64. It is also found that as the number of iterations is increased the restored image quality also increases considerably. The effect of the number of iterations versus PSNR in db is given in Figure 6.5. From the Figure, it is evident that the proposed approach performs significantly better as the number of iterations increases. PSNR in db Number of iterations Figure 6.5 Number of iterations versus PSNR A few experiments were also conducted using degraded images of low information (Lena image), medium information (cameraman image) and large information (crowd). Figure 6.6 shows the large information image degraded with 0.8 noise probability and the corresponding restored image is shown in Figure 6.7.

10 144 PSNR = 49.57db Figure 6.6 Image degraded by impulse noise Figure 6.7 Restored image Figure 6.8 shows the degraded medium information image with 0.8 noise probability and the restored image are shown in Figure 6.9. PSNR = 49.34db Figure 6.8 Image degraded by impulse noise Figure 6.9 Restored image A graph is plotted between number of iterations and MSE and is shown in Figure 6.10 for low information, medium information and large information images.

11 More information image Medium information image less information image MSE MSE Number of iterations Number of iterations Figure 6.10 Number of iteration versus MSE for low information, medium information and large information images For the three types of images, the MSE is minimized as the number of iterations increases. The same network is also used for the restoration of colour images. Colour images are divided into RGB distribution. Then each subspace can be regarded as a gray image space and is processed by counter propagation neural network used in gray images. Finally, they are combined to get a restored colour image. In the first experiment, the image is degraded using impulse noise. Figure 6.11 shows the image degraded by impulse noise and the corresponding restored image is shown in Figure 6.12.

12 146 PSNR = db Figure 6.11 Image degraded by impulse noise Figure 6.12 Restored image A blurred sail boat is shown in Figure 6.13 and the restored image using full CPNN is shown in Figure PSNR = db Figure 6.13 Blurred sail boat Figure 6.14 Restored image In another experiment Lena image is degraded with Gaussian noise of standard deviation σ = 0.5 and is shown in Figure The corresponding restored image is shown in Figure PSNR = 41.89db Figure 6.15 Degraded image with σ = 0.5 Figure 6.16 Restored image

13 147 In another experiment Lena image is degraded with mixed noise (σ = 0.5, p = 0.5) and is restored by full CPNN. Figure 6.17 shows the image degraded by mixed noise and the corresponding restored image is shown in Figure PSNR = db Figure 6.17 Degraded image with mixed noise Figure 6.18 Restored image Table 6.1 gives the processing time taken by the proposed CPN and the resultant PSNR for different colour images like Lena, Mandrill and parrot corrupted with impulse noise of p=0.6. Table 6.1 Processing time in seconds for different colour images for impulse noise Image Processing time in seconds PSNR of restored image (db) Lena Mandrill Parrot

14 CONCLUSION In this chapter, a Full Counter propagation network is proposed for restoring colour images. It was found that the quality of the restored image gets improved when the numbers of iterations are increased. The restored images obtained with this approach are of good visual quality with higher PSNR. The average time taken by this approach to restore the degraded colour images was about 26 seconds, but the visual quality of the image is about 3 db more than the proposed MLMNN.