Adaptive Fuzzy Approach to Gaussian Noise Removal in Gray Scale Images

Visual information transmitted in the form of digital images is becoming a major method of communication in the modern age, but the image obtained after transmission is often corrupted with noise. The received image needs processing before it can be used in applications. A New Fuzzy Filter that adopts Fuzzy Logic is proposed in this paper which removes Gaussian Noise from the Corrupted Gray scale Images. The main concern of the present filter is to distinguish between local variations due to noise and due to image structure. It uses 14 fuzzy rule based convolution mask on every pixel of the image. Objective performance of the proposed algorithm is compared with conventional methods based on Mean Square Error (MSE), Root Mean Square Error (RMSE), Signal to Noise Ratio (SNR) and Peak Signal to Noise Ratio(PSNR). The results illustrate that the proposed method can be used as an effective Noise removal method for Deepinder Kaur ,Baljit Singh, The International Journal of Computer Science & Applications (TIJCSA) ISSN – 2278-­‐1080, Vol. 1 No. 9 November 2012 © 2012, http://www.journalofcomputerscience.com -­‐ TIJCSA All Rights Reserved 10 Gaussian noise. Results show that by using the proposed method improved SNR and PSNR and minimized MSE and RMSE are achieved. Hence proposed algorithm leads to better image enhancement. Keywords: Fuzzy logic; Gray scale; Median Filter; Mean Filter; Gaussian noise; Impulse noise; Multiplicative Noise; Correction term. 1. Introduction Digital images are used in various applications in today’s life. Digital images are corrupted by noise during image acquisition or transmission process. There are different types of noises in digital images. For example, Additive white Gaussian noise (AWGN) is due to image sensors operating at low light levels, poor image acquisition or by transferring the image data in noisy communication channels. Gaussian noise is statistical noise that has its probability density function equal to that of the normal distribution, which is also known as the Gaussian distribution. In other words, the values that the noise can take on are Gaussian-distributed. Gaussian noise is properly defined as the noise with a Gaussian amplitude distribution. This says nothing of the correlation of the noise in time or of the spectral density of the noise. Labeling Gaussian noise as 'white' describes the correlation of the noise. It is necessary to use the term "white Gaussian noise" to be precise. Gaussian noise is sometimes misunderstood to be white Gaussian noise, but this is not the case. Noise is modeled as additive white Gaussian noise (AWGN), where all the image pixels deviate from their original values following the Gaussian curve. That is, for each image pixel with intensity value f ij (1 ≤ i ≤ m, 1 ≤ j ≤ n for an m x n image), the corresponding pixel of the noisy image g ij is given by, (1) where, each noise value n is drawn from a zero -mean Gaussian distribution as shown in fig 1. Deepinder Kaur ,Baljit Singh, The International Journal of Computer Science & Applications (TIJCSA) ISSN – 2278-­‐1080, Vol. 1 No. 9 November 2012 © 2012, http://www.journalofcomputerscience.com -­‐ TIJCSA All Rights Reserved 11 Fig 1. Gaussian Distribution Curve Denoising is the pre-processing step in the Image Enhancement process. Denoising is necessary and first step to be taken before the image data is analyzed for further use. Because after introducing the noise in image, the important details and features of image are destroyed. It is necessary to apply efficient denoising technique to compensate for such data corruption. Image denoising is used to remove the noise while retaining as much as possible the important signal features. The purpose of image denoising is to estimate the original image from the noisy data.