add & mult noises

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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: