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# Class Note for ECE 482 at UA-Comp Visn Dig Image Proc(5)

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Date Created: 02/06/15

Computer Vision amp Digital Image Processing Image Restoration and Reconstruction Electrical amp Computer Engineering Dr D J Jackson Lecture 11 1 Image restoration Restoration is an objective process that attempts to recover an image that has been degraded A priori knowledge ofthe degradation phenomenon Restoration techniques generally oriented toward modeling the degradation Application of the inverse process to recover the original image Involves formulating some criterion criteria of goodness that is used to measure the desired result Electrical amp Computer Engineering Dr D J Jackson Lecture 11 2 Image restoration continued Removal of blur by a deblurring function is an example restoration technique We will consider the problem only from where a degraded digital image is given Degradation source will not be considered here Restoration techniques may be formulated in the Frequency domain Spatial domain Electrical amp Computer Engineering Dr D J Jackson Lecture 11quot Image degradationrestoration process Given gXy some knowledge about H and some knowledge about the noise term the objective is to produce an estimate ofthe original image The more that is known about H and the noise term the closer the estimate can be Various types of restoration lters are used to accomplish this fxy f3 gxy Restoration fxy H filters Noise 770 y Electrical amp Computer Engineering Dr D J Jackson Lecture 114 Image degradationrestoration process If H is a linear position invariant process then the degraded image can be described as the convolution of h and fwith an added noise term gx y hx y f xy 77x y hXy is the spatial domain representation of the degradation function In the frequency domain the representation is GuvHuvFuvNuv Each term in this expression is the Fourier transform of the ofthe corresponding terms in the equation above Electrical amp Computer Engineering Dr D J Jackson Lecture 11 v5 Noise models Common sources of noise Acquisition Environmental conditions heat light imaging sensor quality Transmission Noise in transmission channel Spatial and frequency properties of noise Frequency properties of noise refer to the frequency content of noise in the Fourier sense For example if the Fourier spectrum of the noise is constant the noise is usually called white noise A carry over from the fact that White light contains nearly all frequencies in the visible spectrum in basically equal proportions Excepting spatially periodic noise we will assume that noise is independent of spatial coordinates and uncorrelated to the image Electrical amp Computer Engineering Dr D J Jackson Lecture 116 Noise probab lty density functions V th respect to the spatial noise term we will be concerned with the statistical behavior of the intensity values May be treated as random variables characterized by a probability density function PDF Common PDFs used will describe Gaussian noise Rayleigh noise Erlang Gammanoise Exponential noise Uniform noise Impulse saltandpepper noise Electrical a cumrmer E lnEErl Dr D l Jacksnn Laclure11r7 Gaussian noise Gaussian normal noise models are simple to consider The PDF of a Gaussian random variable 2 is given to the right as In this case approximately 70 of the values of 2 will be within within one standard deviation Approximately 95 of the values of 2 will be within within two standard deviations 1 1 2 2 27m pz where 2 represents intensity 2 represents the mean average value of z G39is the standard deviation 0392 is the variance of z m r Electrical a cumrmer E lnEErl Dr D l Jacksnn Ladure 1173 Rayleigh noise The PDF of Rayleigh noise is given as W graf ti furzza n furz lt41 where zrepresentsmtensxty 5 em 52 been 4 Note the displacement by a horn the origin The basic shape ofthis PDF is skewed to the right 7 Can be usefui m approximating skewed histograms mm 1 7 Rm iuigh IT Elaclncd a cumme Enmnemn m n l Jmmn Lennie 1179 Erlang Gamma noise The PDF of Erlang noise is given as e be if for z 2 0 W 1271 0 for z lt 0 where z represents intensity 2 b a 172 b a2 a gt 0 b is a positive integer 01 K iummu we iu Elaclncd a cumme Enmnemn m n l Jmmn Le um11e1 Exponential noise The PDF ofexponential noise is given as Z 7 a2 forz 20 p 0 forzlt0 II I iii wer z representsintensity 21a 039 71m a gt 0 This PDF is a special case ofthe Erlang PDF with b1 an ch flannel a emunu z mlmn m n J Incl1n Lemmm Uniform noise The PDF ofuniform noise is given as U nilm m izi 1 l iquot If a g 2 g 27 I 7 pz 17 7 a 0 otherwise where z representsintensity a 17 2 a b 7 a 12 i7 flannel a emunu z mlmn m n J Incl1n Lamne1142 Impulse saltandpepper noise The PDF of bipolar impulse noise is given as Paforza 172 P21 orzb 0 otherwise llllplllxc If bgta then any pixel with intensity b will appear as a light dot in the image Pixels with intensity 3 will u I appear as a dark dot u Elcclnczl a Cnmrluler Enmnccnnu m n l Jacksnn Laclure 11713 Example noisy images Elcclnczl a Cnmrluler Enmnccnnu m n l Jacksnn Laclure 11715 Example noisy images continued m m wAhmu x u 1 L 1 new 5 mm m 4 WWW mummy mm mm upuuun mmmm m m m Ele nczl a Cnmrluler Enmneennu m n l Jacksnn Laclure11r15

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