The automatic method to determine a optimal constant of wavelet threshold function of minFDR for...

7/31/2019 The automatic method to determine a optimal constant of wavelet threshold function of minFDR for mitigating int

1/6

VCCA-2011

VCCA-2011

The automatic method to determine a optimal constant of wavelet threshold

function of minFDR for mitigating interference application

to industrial systems

(1) (2)(1)ng [email protected]

(2)Vin Nghin c n t, Tin hc, Tng Ha, H Ni, [email protected]

tr da tr wat tr t tr d rta tr t trong phn t t k p t rt

a a ra t ppp t att tr d t t t pt ta dr rat- ak tr t

pAbstractThere are 3 steps in de-noise by wavelet

thresholding. The second step is very

important. It determines threshold value and

using threshold function to mitigates noise

coefficients. The exactitude and confidence

in the analysis, appraise of signal is

dependent on this step. The paper proposes a

automatic method to determine a optimal

constant of wavelet threshold function using

minimize of the false discovery rate ruleminFDR for mitigating interference

application to industrial systems.

K hi aw atw at tr (.) x x k p

1W a tr at t a a

k t a

i t a

)(mp t t t

N d t L1 t atL2 d NL 22 log

h, g a at 1(.) Hm phn b tch lu ca phn b chuna t tr

C SNR Signal Noise Rate

DWT Decrete Wavelet Transform

IDWT Inverse DWT

TIDWT Translation Invariant DWT

1. r at s c gi tr ln mangnhiu thng tin v tn hiu (thng tin hu ch) cn cch s nh mang t thng tin c ch m ch yu linquan ti nhi ta tng s dng thut loi b cc h s mang nhi a t toli tn hiu gc bng bi c wavelet.P pp ng wavelet thc hin qua a c a :

-c mt l bi i thu at ccc h s bi i wavelet.

- a nh gi trng v s dng c b cc h s nhiu.

-c ba l bi at khi phctn hiu.Ca u quan trng trong qu trnh x l tnhiu. x tin cy trong phn tch, u qu kh nhiu phthuc rt nhi bc hai. u tin trong kh nhiu l chn wavelet chobi i thu c wavelet. Sau khi bi ithu at c cc h s w, thc hin giithut c cc gi tr ng w :

)/( ww (1)

hoc: )( ww

, (2)

tr l gi trng, ng v ng ca lch chun nhiu. Cc bin

62
mailto:[email protected]:[email protected]


2/6

VCCA-2011

VCCA-2011

php kh nhiu khc nhau vic chn (.), v . ng s quyt nh vic p d ivi tn hi t ng nhiu quyt nhmc nhiu v gi tr nh t cc lut

c cui cng ca kh nhiu l bi ic wavelet cho cc h s w k p thiu:

wWx 1 (3)

2. Ph -N [1]

tr : )4(log2 N

p d t (1). N t t t t p t garit trong tr nh b p t

t t k- SURE[2] tr t ra t a k t t t a p N t p t tr t :

),(minarg0 ll

wSURE (5)

wl l c at tt SURE(,wl) a k t P pp k p a a tr a k t - Bayes [3]

N t t p :

s

l

2

, (6)

r 2 p a 2s

l

p a t t :

)0,max( 22 xs

(7)

tr

lN

nnlx

wN 1

22 1 (8)

p a a d Nl

wavelet wn p 22

x th

:1 = max(wn) (9)

tt k t t 2).- minFDR[4]

N tr k a t a tr t t d t t tr N at n tr t t tr p:

)]/(1[2 wpn (10)

Sa p p tr pn:

)(...)2()1( Nppp (11)

Bt = :

qN

nnp )( (12)

a:

2

)(1 1

mp (13)

N k a t t P k ta p d [4], [5], [6], t t p t t a t a at t tr 7 t k t a k t a, t tr = :

)14(2

)(

11

.

.

).1.(

mp

ia

r : tr t c tnh

phn b nhi k t a tr i

p a t a nh t matr a at t a a a tr p t a t tr 7 a y gi tr bng 2.Trong bi ny chng ti s trnh by c th tt t t s a ny. Gi tra c xc nhvi m t kt tt t t

p t d t t a:

- : at .

- : p t t t t tn hi t M (3,4,5,6,7,8).

- 3: t k t N- 4: d - : a k

a t tr tr tr SN rt tp

- 6: d t tr p p a

- 7: tr t - 8: SNR tr t

SN a (4). tr - : a t k

t tr t t (3, t M tn hiu.

- : tp t t t a at k, a a t t .

- : a tt L*M pc a SN t.P pp a tt t t tr t

at tr t tr ra a:

63


3/6

VCCA-2011

VCCA-2011

t at

- To tn hiu v nhiu kch tc N- Chn b l k tc L1

- Tnh cc h s lc: h, g- c dch vng L2

i = 0

Dch vng phi cc mu tn hiu

- ng thch nghi

2

)(11..).1.(

mp

ia

W c cc h s wk

a=1:1:10

Ch ng

0

-Tnh cc gi tr hp bi p a

IDWT khi phc tn hiu

Dch vng tri cc mu tn hiu khi phc

i=i+1

i = L2 ?

1

Ly trung bnh tn hiu

S SN SN

Kt thc

1

0

p p SNR SN

p t : M tn hiu

- x

a SNR max

64


4/6

VCCA-2011

VCCA-2011

3. t t a a tr k t u. Ba t t Doppler t

tr t ata, t k ta t t tr tr pka t tha t k a t t t t t. at k ad t k p ta d t pt a pp at at kt k a t t a= t t k t SN k - u Doppler

0 100 200 300 400 500

-1.5

-1

-0.5

0

0.5

1

1.5

Tin hieu goc

-

0 100 200 300 400 500

-1.5

-1

-0.5

0

0.5

1

1.5

Tin hieu co nhieu

b-

SNR = 9.2274 dB

0 100 200 300 400 500

-1.5

-1

-0.5

0

0.5

1

1.5

Tin hieu khu nhieu DWT

-

SNR = 13.3442dB

0 100 200 300 400 500

-1.5

-1

-0.5

0

0.5

1

1.5

Tin hieu khu nhieu nguong thich nghi minFDR a=3

-

SNR = 13.3701dB

0 100 200 300 400 500

-1.5

-1

-0.5

0

0.5

1

1.5


-

SNR = 10.9215dB

0 100 200 300 400 500

-1.5

-1

-0.5

0

0.5

1

1.5


-

SNR = 9.3289dB

0 100 200 300 400 500

-1.5

-1

-0.5

0

0.5

1

1.5


-

SNR = 14.7669dBt t k tr t ppr t a= t SN a t k tt t k- i

65


5/6

VCCA-2011

VCCA-2011

0 50 0 1 0 00 1 50 0 20 0 0 2 5 00 3 00 0 3 50 0 40 0 0 4 5 0010 0

20 0

30 0

40 0

50 0

60 04320 mau tin hieu dien

H3 -

0 100 200 300 400 500 600100

150

200

250

300

350

400

450

500

Tin hieu Dien tron nhieu

H3b

SNR = 24.6001dB

0 100 200 300 400 500 60100

150

200

250

300

350

400

450Tin hieu Dien khu nhieu nguong deu

H3

0 100 200 300 400 500 60050

100

150

200

250

300

350

400

450Tin hieu Dien khu nhieu nguong thich nghi minFDR a=3

H3

0 100 200 300 400 500 600100

150

200

250

300

350

400


H3

a=4, SNR=26.9690dB

0 100 200 300 400 500 60050

100

150

200

250

300

350

400


H3f =26.9690dB

0 100 200 300 400 500 60050

100

150

200

250

300

350

400


H3g

=29.9780dB

- C

0 0.5 1 1.5 2 2.5

x 104

-1

0

1

2

3

4

5

622087 mau tin hieu do khi CH4

H4 -

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2

1.4512 mau (3000-3511) tin hieu do khi CH4

H4b

SNR = 24.3218dB

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2

1.4Tin hieu thuc khu nhieu nguong deu

H4

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2

1.4Tin hieu thuc khu nhieu nguong thich nghi minFDR a=

H4

66


6/6

VCCA-2011

VCCA-2011

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2

1.4Tin hieu thuc khu nhieu nguong thich nghi minFDR a=4

H4

=30.4424dB

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2


H4f

=27.3075dB

0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

1.2


H4g

=34.2258dB tr p t t t t t k kt t t t d tr t k t a= t t tt tr t SN a

p pp tr t k

4. r t t tt t tr p d d t d k a tr a a t k t a= tr k a tr a= t a kt

p tr t r tt t ch s a t a= tc ca nhm tcgi xut l:

2

)(11..).1.(2

mp

i

N p pp k

tr t kt k tnghi wavelet minFDR ( a=) t tr tr SNR a t

t k p tr tr da t ra k t d ra

[1] D. Donoho, I. M. Johnstone: Ideal SpatialAdaptation by Wavelet Shrinkage, Department of

Statistics, Stanford University, USA. April 1993.

[2] Donoho, D.L., Johnstone, I.M.: Adapting to

unknown smoothness via wavelet shrinkage.

Department of statistics Stanford university, USA,

1994.[3] Sanyam Anand1, Amitabh Sharma, Akshay

Girdhar: Undecimated Wavelet Based New

Threshold Method for Speckle Noise Removal in

Ultrasound Images. IACSIT Press, Singapore

2011.

[4] V.V.K.D.V. Prasad, P.Siddaiah and B.PrabhakaraRao: Denoising of Biological Signals Using

Different Wavelet Based Methods and Their

Comparison. Asian Journal of Information

Technology 7 (4): 146-149, 2008.

[5] David Donoho and Jiashun Jin: Asymptotic

minimaxity of false discovery rate thresholding

for sparse exponential data. The Annals of

Statistics, Institute of Mathematical Statistics,

Vol. 34, No. 6, 2980 -3018, 2006.

[6] Martina Pavlicova, Thomas J. Santner and Noel

Cressie: Detecting signals in FMRI data usingpowerful FDR procedures. Statistics and Its

Interface Volume 1, 2332, 2008.[7 r N r P

: . t tr COMNAVI 2011, 142-147, 2011

r t tt

tt t t tr a t

N a a - t tr ra a t t

N tt k t t k p

67

The automatic method to determine a optimal constant of wavelet threshold function of minFDR for...

Documents

Transcript of The automatic method to determine a optimal constant of wavelet threshold function of minFDR for...