Image Restoration

ReferenceGonzalez and Woods, Digital Image

Processing, 2nd Ed, Prentice Hall, 2002.

Khan IftekharuddinISIP Lab

ISIP Lab/KMI

Image RestorationImage Restoration

ISIP Lab/KMI

•pdf of Gausssian random variable z:

70% of values are in [(µ-σ),(µ+σ)]

95% of values are in [(µ-2σ),(µ+2σ)]

•pdf of Rayleigh noise:

Noise ModelsNoise Models

22 2/)(

21)( σµ

σπ−−= zezp

44(4/

:var,0

,)(2)(

2

/)( 2

πσπµ −=+=

≤

≥−=−−

bandba

areianceandmeanTheazfor

azforeazbzp

baz

ISIP Lab/KMI

Noise ModelsNoise Models

Erlang (Gamma) noise pdf:2

2

1

;0,0

0,)!1()(

aband

ab

zfor

zforebza

zpaz

bb

==

<

≥−=

−−

σµ

Uniform noise pdf:12

)(,2;,0

,1)(

22 abba

otherwise

bzaifabzp −

=+=

≤≤

−= σµ

Impulse (salt-and-pepper) noise pdf:

.;,0,,

)( dotlightaasappearwillblevelgrayabIfotherwise

bzforPazforP

zp b

a

−>

==

=

ISIP Lab/KMI

Noisy ImagesNoisy Images

ISIP Lab/KMI

Noisy ImagesNoisy Images

ISIP Lab/KMI

Noisy ImagesNoisy Images

ISIP Lab/KMI

Additive Noise RemovalSpatial Filtering

Additive Noise RemovalSpatial Filtering

Arithmetic Mean filter

∑∈

=xySts

tsgmn

yxf),(

),(1),(

Similar to convolution mask. Sxy is the nxn filter

Geometric mean filtermn

Sts xy

tsgyxf

1

),(

),(),(

= ∏

∈

Harmonic filter

∑∈

=

xySts tsg

mnyxf

),( ),(1),(

ISIP Lab/KMI

Additive Noise RemovalSpatial Filtering

Additive Noise RemovalSpatial Filtering

Contraharmonicmean filterQ ->order of filter

For +ve->removes pepper noise

For –ve->removes salt noise

For Q=0 ->arithmetic

For Q=-1 -> mean

∑

∑

∈

∈

+

=

xy

xy

Sts

QSts

Q

tsg

tsgyxf

),(

),(

1

),(

),(),(

ISIP Lab/KMI

Spatial FilteringSpatial Filtering

ISIP Lab/KMI

Order-Statistics FiltersOrder-Statistics Filters

Filters

Median

Max and Min

Midpoint

ISIP Lab/KMI

Spatial FiltersSpatial Filters

ISIP Lab/KMI

Spatial FiltersSpatial Filters

Alpha trimmed mean filter

levelsgraytotaldtsgdmn

yxfxyStsr ;),(1),(

),(∑∈−

=

ISIP Lab/KMI

Adaptive Spatial FilteringAdaptive Spatial Filtering

ISIP Lab/KMI

Frequency filtersFrequency filters

ISIP Lab/KMI

Butterworth FilteringButterworth Filtering

ISIP Lab/KMI

Frequency FiltersFrequency Filters

ISIP Lab/KMI

Frequency filteringFrequency filtering

ISIP Lab/KMI

Interference noiseInterference noise

ISIP Lab/KMI

Degraded ImpulseDegraded Impulse

ISIP Lab/KMI

Turbulence NoiseTurbulence Noise

6/5)^2^2^{exp( vuk +−Turbulence Model

ISIP Lab/KMI

Blurred Image Restoration - IFBlurred Image Restoration - IF

ISIP Lab/KMI

Motion Blur onlyMotion Blur only

ISIP Lab/KMI

Inverse and least mean square (wiener) FilteringInverse and least mean square (wiener) Filtering

ISIP Lab/KMI

Motion Blur+ noiseIF and wiener filteringMotion Blur+ noise

IF and wiener filtering

ISIP Lab/KMI

Constrained least square filteringConstrained least square filtering

ISIP Lab/KMI

Iterative Constrained least square filteringIterative Constrained least square filtering