TAILIEUCHUNG - The Essential Guide to Image Processing- P6

The Essential Guide to Image Processing- P6:We are in the middle of an exciting period of time in the field of image processing. Indeed, scarcely a week passes where we do not hear an announcement of some new technological breakthrough in the areas of digital computation and telecommunication. | TA Types of Noise and Where They Might Occur 149 TYPES OF NOISE AND WHERE THEY MIGHT OCCUR In this section we present some of the more common image noise models and show sample images illustrating the various degradations. Gaussian Noise Probably the most frequently occurring noise is additive Gaussian noise. It is widely used to model thermal noise and under some often reasonable conditions is the limiting behavior of other noises . photon counting noise and film grain noise. Gaussian noise is used in many places in this Guide. The density function of univariate Gaussian noise q with mean and variance r2 is pq x 2 2 1 2e x for to x to. Notice that the support which is the range of values of x where the probability density is nonzero is infinite in both the positive and negative directions. But if we regard an image as an intensity map then the values must be nonnegative. In other words the noise cannot be strictly Gaussian. If it were there would be some nonzero probability of having negative values. In practice however the range of values of the Gaussian noise is limited to about 3 r and the Gaussian density is a useful and accurate model for many processes. If necessary the noise values can be truncated to keep f 0. In situations where a is a random vector the multivariate Gaussian density becomes pa a 2 - 2 S -1 2 e a a-l G where E a is the mean vector and 2 E a fi a m is the covariance matrix. We will use the notation a N 2 to denote that a is Gaussian also known as Normal with mean l and covariance 2. The Gaussian characteristic function is also Gaussian in shape Oa u eU -uT tu 2. FIGURE The Gaussian density. 150 CHAPTER 7 Image Noise Models The Gaussian distribution has many convenient mathematical properties and some not so convenient ones. Certainly the least convenient property of the Gaussian distribution is that the cumulative distribution function cannot be expressed in closed form using elementary functions. However it

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