eurocon2009 apalkov

IMPROVED SWITCHING MEDIAN FILTER FOR IMPULSE NOISE REMOVAL

Denis K. Kuykin, Vladimir V. Khryashchev, Ilya V. Apalkov

e-mail: connect@piclab.ru

P.G. Demidov Yaroslavl State UniversityDigital Circuits and Signals Laboratory

2

Agenda

1. Introduction

2.Proposed Algorithms

3.Research Results for Salt-and-Pepper Noise

4.Research Results for Random Valued Impulse Noise

5.Conclusion

3

Classic Median Filtering

20% salt-and-pepper noise median filter (5×5 mask size)

4

Introduction

The problem is

• to develop modified algorithms based on rank-order statistics and switching

schema for restoration of digital images corrupted with salt-and-pepper and

random valued impulse noises

• to compare proposed algorithms with known ones

Conditions to the algorithms:

• effectiveness with wide range of noise ratio

• reasonable computational complexity

• efficient impulse noise removal

• preservation of object edges

5

Peak Signal to Noise Ratio

N

iiixN

PSNR

1

2

2

)(1

255lg10

ix − restored image pixel value

i − original image pixel value

N − image pixels number

6

Image Quality Criteria Correlation withHuman Estimation

Distortion type

Image quality metrics

PSNR UIQ SSIM PSNR-M UIQ-M VIF

Gaussian blurring 0,7428 0,7135 0,6514 0,8563 0,8592 0,9077

JPEG 0,4882 0,7762 0,6223 0,8129 0,8608 0,8784

JPEG2000 0,8428 0.8170 0,8433 0,9063 0,8965 0,9467

Impulse noise 0,944 0,8824 0,8959 0,9445 0,8736 0,9624

Additive Gaussian noise

0,9478 0,9184 0,9397 0,9497 0,9239 0,9552

Averaged value 0,7931 0,8226 0,7905 0,8939 0,8828 0,9301

7

Switching Image Restoration Schema

corrupted image

restored image

preliminary detection step

filtration procedure

8

Proposed Algorithms

1. Modified Progressive Switching Median Filter for Salt-and-Pepper Noise Removal

2. Modified Progressive Switching Median Filter for Random Valued Impulse Noise Removal

9

Salt-and-Pepper Impulse Noise Model

)(1

255

0

pni

p

n

i

ppyprobabilitwith

pyprobabilitwith

pyprobabilitwith

x

ix - corrupted image pixel values

i - original image pixel values

np - negative impulses density

pp - positive impulses density

10

Salt-and-Pepper Impulse Noise Model(known restoration algorithms)

CLASSICAL MEDIAN FILTER

• preserves object edges• misses a lot of noisy pixels• corrupts “good” image pixels

PROGRESSIVE SWITHING MEDIAN FILTER (PSM)(Wang Z., Zhang D. Progressive switching median filter for the removal of impulse noise from highly corrupted images, IEEE Trans. on Circuits systems – II (1) (1999). V. 46, pp. 78-80.)

• preserves object edges• is unable to remove blotches from highly corrupted images

ADAPTIVE MEDIAN FILTER (AMF)

• removes blotches from highly corrupted images• often corrupts object edges• high computational complexity

11

Proposed MPSM Algorithmfor Salt-and-Pepper Noise Removal

(noise detector)

}{ ix

}{ if

DWW

}|min{min Wiji jx

}|max{max Wiji jx

1

0

maxmin

i

i

iii

felse

fthen

xif }{ f

noise detection

result

}{ ix − input corrupted image }{ if − binary matrix

12

Proposed MPSM Algorithmfor Salt-and-Pepper Noise Removal

(filtration procedure)

}{}{ 0 xx }{}{ 0 ff FWW

}|{ 1 Wi

nj

ni jxmedmed

Wij

njfM 1

11

21

,

0,

1

ni

ni

ni

ni

ni

ni

ni

ni

ffxxelse

fmedxthen

WMandfif }{ f

restored image

}{ 1nix

}{ 1nif

i

nifK

0K

0K

13

Comparative Analysis of Efficiency(classic algorithms)

14

Comparative Analysis of Efficiency(algorithms with detector)

0 10 20 30 40 50 60 70 8010

15

20

25

30

35

40

45

50

p, %

PS

NR

, dB

PSM

MPSM

15

Visual Analysis

Original image 20% salt-and-pepper noise(PSNR = 10.68 dB)

16

Visual Analysis

AMF(PSNR = 33.94 dB)

MPSM(PSNR = 36.77 dB)

17

Highly Corrupted Image Restoration

50% salt-and-pepper noise(PSNR = 8,45 dB)

MPSM(PSNR = 33.22 dB)

18

Highly Corrupted Image Restoration

80% salt-and-pepper noise(PSNR = 6.42 dB)

MPSM(PSNR = 25.83 dB)

19

Random Valued Impulse Noise Model

pprobablitywith

pprobablitywithzx

ii 1,

,

ix - corrupted image pixel values

i - original image pixel values

p - noise density

z - uniformly distributed random value

20

Random Valued Impulse Noise Model(known restoration algorithms)

ADAPTIVE CENTRAL WEIGHTED MEDIAN FILTER (ACWM)(Chen T., Wu H. Adaptive impulse detection using center-weighted median filters // IEEE Signal Processing Letters, 2001. V. 8, № 1. P. 1-3. )

• provides good results if noise density is small

SIGNAL DEPENDED RANK ORDERED MEAN FILTER (SDROM)(Abreu E., Mitra S. A signal-dependent rank ordered mean (SD-ROM) filter-a new approach for removal of impulses from highly corrupted images // Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP’95), 1995. V. 4, P. 2371-2374. )

• preserves object edges• provide relatively good visual perceived quality• removes blotches from highly corrupted images

DIRECTED WEIGHTED MEDIAN FILTER (DWM)(Dong Y., Hu S. A new directional weighted median filter for removal of random-valued impulse noise // IEEE Signal Processing Letters, 2003. V. 14, № 3. P. 193-196. )

• often loose effectiveness if noise density is high

• may blur tiny objects on image

21

Random Valued Impulse Noise Detectors Comparison

p 10% 20% 30%

missfalse-

hitmiss

false-hit

missfalse-

hit

DWM 5216 2212 8607 4217 10396 6715

ACWM 3372 1514 8134 1553 14351 2110

SDROM 3523 4501 7257 5119 10962 6749

miss – number of corrupted pixels missed by detector

false-hit – number of noise-free pixels marked by detector as corrupted

22

Proposed MPSM Algorithmfor Random Valued Impulse Noise Removal

(noise detector)

}{ ix

}{ if

DWW

}|),1({ Wiji

wi jxwxmediany

0

1

:

i

i

kk

felse

fthen

Tdkif }{ f

noise detection

result

}{ ix − input corrupted image }{ if − binary matrix

12 kwwiik yxd

23

Proposed MPSM Algorithmfor Random Valued Impulse Noise Removal

(filtration procedure)

}{}{ 0 xx }{}{ 0 ff FWW

}|{ 1 Wi

nj

ni jxmedmed

Wij

njfM 1

11

21

,

0,

1

ni

ni

ni

ni

ni

ni

ni

ni

ffxxelse

fmedxthen

WMandfif }{ f

restored image

}{ 1nix

}{ 1nif

i

nifK

0K

0K

24

Random Valued Impulse Noise Removal Results

0 2 4 6 8 10 12 14 16 18 2031

32

33

34

35

36

37

38

39

40

41

p, %

PS

NR

, dB

Median

SDROMDWM

MPSM

25

Visual Results

15% random valued impulse noise(PSNR = 17,47 dB)

SDROM(PSNR = 34,70 dB)

26

Visual Results

DWM(PSNR = 35,28 dB)

Proposed Algorithm(PSNR = 35,91 dB)

27

More…

The MPSM algorithm for random valued impulse noise removal is described in more details in the paper:

D. Kuykin, V. Khryashchev, A. Priorov. DETECTION AND RESTORATION OF RANDOM-VALUED IMPULSE NOISE CORRUPTED PIXELS

which was submitted to participate in The 2009 International Workshop on

Local and Non-Local Approximation in Image Processing (LNLA’2009)

Also this paper, MatLab code and all results can be downloaded from

http://www.piclab.ru/research/mpsm.html

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PICLAB(www.piclab.ru)

PICLAB – is the advanced tool for image restoration and research of image processing algorithms

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Conclusion

Proposed modified algorithm for salt-and-pepper impulse noise removal based on switching schema and rank ordered statistics provide about 1-2 dB PSNR increasing relative to another filters

Proposed MPSM algorithm for restoration of images corrupted by random valued impulse noise provides more performance in image restoration which is expressed in 0.5 dB PSNR increasing.