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Additive & Multiplicative Noises
Noise present in an image either in an additive ormultiplicative form .
Additive noise follows : w ( x , y ) = s ( x , y ) + n( x , y ), Multiplicative noise satisfies : w ( x , y ) = s ( x , y ) × n( x , y ),
here , s ( x ,y ) original signal,n( x, y ) noise introduced into the signal to produce thecorrupted image w ( x, y ), and( x, y ) pi!el location. "mage alge#ra is done at pi!el level."mage multiplication changes intensit$ of the image.
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Gaussian Noise %aussian noise is evenl$ distri#uted over the signal .&his
means that each pi!el in the nois$ image is the sum of thetrue pi!el value and a random %aussian distri#uted noisevalue. %aussian distri#ution has a #ell shaped pro#a#ilit$distri#ution function given #$ ,
where g represents the gra$ level, m is the mean or averageof the function, and ' is the standard deviation of the noise.%raphicall$, it is represented as shown in igure
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Salt and Pepper Noise
*alt and pepper noise is an impulse t$pe of noisecaused generall$ due to errors in data transmission"t has onl$ two possi#le values . &he pro#a#ilit$ of each ist$picall$ less than . . &he corrupted pi!els are set
alternativel$ to the minimum or to the ma!imum value,giving the image a -salt and pepper li/e appearance.0naffected pi!els remain unchanged. or an 12#it image,the t$pical value for pepper noise is and for salt noise344.%enerall$ caused #$ malfunctioning of pi!el elements inthe camera sensors, fault$ memor$ locations, or timingerrors in the digiti5ation process.
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PDF for Salt and Pepper Noise
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Salt and Pepper Noise (Contd..)
*alt and pepper noise with a variance of . 4 is shown inigure
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Speckle Noise*pec/le noise is an e!ample of multiplicative noise.
6ccurs in laser and *A7 (*$nthetic Aperture 7adar) data.*pec/le noise follows a gamma distri#ution and is given as
where variance is a 3 8 and g is the gra$ level.&he gamma distri#ution is given #elow
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Speckle Noise (Contd..)
6n an image, spec/le noise (with variance . 4) loo/sas shown in igure 3
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1 f Noise (!ro"nian Noise)
&he mathematical model for 9 f noise is fractionalrownian motion.
rownian motion is a non2stationar$ stochastic process
that follows a normal distri#ution ."t can #e graphicall$ represented as shown in igure ;
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!ro"nian Noise (Contd..)6n an image, rownian noise would loo/ li/e figure <
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#$er%al Noise&he amount of thermal noise to #e found in 5#andwidth in an actual device is given as:
N + = /& ( 9 5) here:
>= olt5mann?s constant ( .;1 ; @ 23; 9>)&=a#solute temperature (>)
At room temperature &=3B >N+ = .;1 ;@3B @ 23; = 2
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%pulse Noise
"mpulse noise is noncontinuous and consists of irregularpulses or noise spi/es of short duration and of relativel$high amplitude.&hese spi/es are often called -hits ."mpulse2noise degrades voice telephon$ onl$ marginall$,if at allE however, it ma$ seriousl$ degrade error rate ondata or other digital circuits.
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SN'
*N7 is e!pressed in deci#els (d )2the amount #$ whicha signal level e!ceeds the noise within a specified#andwidth.&he following are the suggested *N7 values for variousservices:Foice: < dFideo: