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# ece542-7 - ECE542-7 Digital Image Processing 5 Image...

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1 ECE542-7 Digital Image Processing 5- Image Restoration Dr. Z. Aliyazicioglu Cal Poly Pomona Electrical & Computer Engineering 1 Cal Poly Pomona Electrical & Computer Engineering Office 9-143 A Model of the Image Degradation/Restoration Process Input image f(x,y), the degraded image g(x,y), some knowledge about the degradation function H, and some ECE542 - 7 2 Cal Poly Pomona knowledge about the additive noise term (x,y) Restoration filter is applied to obtain an estimated f(x,y) of the original image Want to estimate to be as close as possible to original image Substitute and yield ^

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2 A Model of the Image Degradation/Restoration Process If H is a linear, position-invariant process, then the degraded image is In the frequency domain (, ) (, ) (, ) gxy hxy fxy xy  (,) (,)(,) Guv HuvFuv Nuv ECE542 - 7 3 Cal Poly Pomona Some Important Noise Probability Density Function Gaussian Noise The PDF of Gaussian random variable, z, is is mean of average value of z is its standard deviation 2 its variance 2 2 () 2 1 2 z pz e  ECE542 - 7 4 Cal Poly Pomona 70% of its value in the range [( - ),( + )]
3 Some Important Noise Probability Density Function Rayleigh Noise The PDF of Rayleigh noise with random variable, z, is The mean is 2 () 2 f o r 0f o r za b pz b  / 4 ab   ECE542 - 7 5 Cal Poly Pomona The variance 2 is 2 (4 ) 4 b Some Important Noise Probability Density Function Erlang (Gamma) Noise The PDF of Erlang noise with random variable, z, is The mean is 1 for () (1 ) ! o r bb az az ez a b b a 0 0 b is integer ECE542 - 7 6 Cal Poly Pomona The variance 2 is 2 2 b a 0

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4 Some Important Noise Probability Density Function Exponential Noise The PDF of exponential noise with random variable, z, is The mean is for () 0f o r az ae z a pz za 1 a 0 0 ECE542 - 7 7 Cal Poly Pomona The variance 2 is 2 2 1 a Some Important Noise Probability Density Function Uniform Noise The PDF of uniform noise with random variable, z, is The mean is 1 if 0o t h e r w i s e azb ba 2 ab ECE542 - 7 8 Cal Poly Pomona The variance 2 is (linear operator) 2 2 12
5 Some Important Noise Probability Density Function Impulse (salt-and-peper) Noise The PDF of impulse noise with random variable, z, is If b>a, gray level b will appear as a light dot in the image and a will appears like a dark dot Usually a and b are saturated values b for () P f o r 0o t h e r w i s e a Pz a p zz a  ECE542 - 7 9 Cal Poly Pomona Usually and are saturated values.

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ece542-7 - ECE542-7 Digital Image Processing 5 Image...

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