color image denoising in wavelet domain using adaptive thresholding incorporating the human visual...

7/28/2019 Color Image Denoising In Wavelet Domain Using Adaptive Thresholding Incorporating the Human Visual System M

1/4


2/4

discontinuities. The wavelet representation naturally facilitates

the construction of such spatially adaptive algorithm, which

compresses the essential of signal into relatively few, large

coefficients. Thresholding methods compare the input to a

given threshold and set it to zero if its magnitude is less

than the threshold. The idea is that coefficients insignificant

relative to the threshold are likely due to noise, whereas

significant coefficients are important signal structures. Thresh-olding essentially creates a region around zero where the

coefficients are considered negligible. Outside of this region,

the thresholded coefficients are kept to full precision. Here

two different adaptive soft thresholding methods are used for

image denoising. These are BayesShrink and Lees threshold.

BayesShrink thresholding technique was proposed by Chang

[1],[2] and Lees thresholding technique was proposed by Lee

[15].

IV. DWT WITH ADAPTIVE THRESHOLDING USING HVS

MODEL

The color image denoising algorithm using HVS is shown in

Fig. 2. First, the RGB color images are converted to CIELABcolor space. CIE L*a*b* (CIELAB) is the most complete color

space which describes all the colors visible to the human eye.

Wavelet transform is a desirable choice for the HVS model

[16]. The CSF can be implemented by modifying the wavelet

coefficients in every sub-band using ISF.

Fig. 2. Denoising Algorithm with HVS Model.

A. CSF implementation in Wavelet Denoising:

The CSF describes the sensitivity of the HVS as a func-

tion of contrast and spatial frequency. The spatial frequency

response of the luminance has the characteristics of band-pass

filter while spatial frequency responses of the Red-Green and

Blue-Yellow channels have the characteristic of low pass filter.

Sensitivity is good for low spatial frequencies, but declines at

higher frequencies.

B. Mapping the CSF curve into DWT coefficients:

Let us assume that an image is optimized with given

resolution r pixels (dots) per inch and a viewing distance v

meters. The spatial sampling frequency fs in pixels per degree

is then given by

fs =2vrtan(0.5)

0.0254(1)

If the signal is critically down-sampled at Nyquist rate,

0.5 cycles per pixel are obtained. That means the maximum

frequency represented in the signal measured in cycles perdegree is fmax = 0.5fs.

The sub-band of level j = 2 and orientation = 2 ishighlighted in Fig. 4. This sub-band contains mostly horizontal

Fig. 3. CSF Curves for Luminance and Chromatic channels.

Fig. 4. Relation between CSF and 5-level 2D Mallat wavelet decomposition

details. The horizontal spatial frequencies of this sub-band

varies from 0 0.25fmax and the vertical frequencies from0.25 to 0.5fmax.The weighting that must be used for thewavelet coefficients in this sub-band is described by portions

of 2D CSF functions.

C. Extracting coefficients for CSF compensation:The CSF is basically used to modify the wavelet coefficients

on the basis of invariant single factor (ISF) [6],[7]. In ISF we

assign a weighting factor into every sub-band. It is supposed

to describe the average sensitivity of the HVS for the covered

frequency range. The weighting factor is used to multiply the

coefficients before wavelet thresholding.

f = (fh, fv) =[(fL, fL), T[w1csf(fL, fH)], T[w

2csf(fH, fL)],

T[w3csf(fH, fH)]] (2)

where wcsf is CSF weighting factor along every orientation

and operator T stands for adaptive thresholding.

To obtain the CSF weighting factors denoted by wcsf foreach sub-band, the CSF curve is sampled at the mid frequency

of the frequency range for each sub-band. The CSF functions

for Luminance proposed by Mannos and Sarkinson [4].

499


3/4

H(fLum) = 2.6(0.192 + 0.114fLum)e[(0.114fLum)

1.1]) (3)

The chromatic curves are given by the following equation

H(fChrom) = exp(afChrom + b) (4)

Where fLum and fChrom are the spatial frequencies with

units of cycles/degree. For RG, a = 0.13 and b = 4.84. ForYB, a = 0.14 and b = 4.22 [17].

The CSF weighting factors are obtained directly from the

CSF curves in the normalized spatial frequency domain. The

image is decomposed into 5 levels, for which a 11-weightsystem is proposed instead of the generally used 6-weightsystem. The 11-weights are derived as follows.

1) For each level of decomposition,the average of the CSF

curve for the frequency range of each HH sub-band as

well as for the corresponding low frequency band is

calculated. Thus, for first level of decomposition, the

average of the CSF curve for frequency range 0.5fmax

fmax is taken and is denoted by p1. The averageof the CSF curve for frequency range 0 0.5fmaxis taken and is denoted by q1. Similarly, for second

level the average of the CSF curve for frequency range

0.52fmax 0.5fmax is taken and is denoted by p2and the average of the CSF curve for frequency range

0 0.52fmax is denoted by q2 and so on upto p5 andq5.

2) The CSF weight for the HH1 sub-band is given by p1,

the HH2 sub-band by p2, and so on. The CSF weight

for the final fifth level LL sub-band is given by q5.

3) The CSF weight for the LH1 and HL1 sub-band is

given by

(p1 q1) , the LH2 and HL2 sub-band by(p2 q2) , and so on.4) Finally, all the 11 weights are normalized so that the

lowest weight equals 1.

Fig. 5 shows the CSF curve for luminance, for a spatial

frequency fs = 64 pixels/degree . The 11 CSF weightsextracted from this curve have been shown in Fig. 6.

Fig. 5. CSF curve for luminance for fs=64 pixels/degree.

The weights thus extracted are multiplied with the wavelet

coefficients to modify the image into a contrast enhanced one.

Fig. 6. CSF mask with 11 unique weights for fs = 64 pixels/degree.

The modified image is then denoised by adaptive thresholding

algorithm applied to the various frequency components ob-

tained by DWT. In this paper , two such thresholding schemes

are used - BayesShrink [1],[2] and Lees Thresholding [15].

The denoised sub-bands are reconstructed to obtain the de-

noised image using Inverse DWT.

V. EXPERIMENTAL RESULTS

The images of LENA, PEPPERS and BARBARA have been

used to test the algorithm. BayesShrink and Lees adaptive

thresholding method have been used for denoising. The results

for different values of noise variance for the two methods are

shown in Table I. The images are viewed in a 19 monitorhaving a screen resolution of 96 pixels(dots)/inch. The viewingdistance is taken to be 55 cm. Biorthogonal 6.8 wavelet is used

in decomposition and reconstruction DWT filters.

TABLE I

PERFORMANCE EVALUATION IN TERMS OF PSNR AN D Q FOR DIFFERENT

TEST IMAGES WITH VARYING PERCENTAGE OF NOISE USING

BAYESSHRINK AND LEE S ADAPTIVE THRESHOLD

IMAGE 2 BayesShrink Lees

PSNR Q PSNR Q

0.03 23.55 0.117 23.88 0.124

LENA 0.05 23.64 0.121 23.21 0.116

0.07 22.55 0.105 22.81 0.118

0.03 21.56 0.166 23.34 0.205

PEPPERS 0.05 20.73 0.152 20.65 0.152

0.07 21.22 0.151 21.48 0.158

0.03 25.81 0.071 25.74 0.073

BARBARA 0.05 24.82 0.069 24.36 0.069

0.07 24.07 0.063 24.32 0.066

In general, the PSNR and Universal Image Quality Index

(Q)[8] of the denoised output image decreases with the in-

crease in noise variance as seen in Table I. Table II shows

the comparison between the traditional 6-weight system andthe proposed 11-weight system. The comparison clearly shows

that the 11-weight system outperforms the 6-weight system

both in terms of PSNR and Q value.It is observed from Fig. 7 and Fig. 8 that incorporation of

CSF provides better image quality by enhancing the contrast.

The comparison of the output images without implementation

500


4/4

TABLE II

COMPARISON OF PERFORMANCES OF 6- WEIGHT AND 11 -WEIGHT

SYSTEMS IN TERMS OF PSNR AN D Q FOR DIFFERENT TEST IMAGES FOR A

NOISE VARIANCE 2 = 0.03 USING BAYESSHRINK AND LEE S ADAPTIVE

THRESHOLD

PSNR Q PSNR Q

IMAGE 6 weights 11 weights

BayesShrink

LENA 23.20 0.10 23.55 0.1168

PEPPERS 22.91 0.17 21.56 0.1658

BARBARA 25.48 0.0662 25.81 0.0707

Lees

LENA 23.73 0.12 23.88 0.1235

PEPPERS 22.62 0.18 23.34 0.2046

BARBARA 24.73 0.0745 25.74 0.0726

(a) (b) (c) (d)

(e) (f) (g) (h)

Fig. 7. Comparison of denoising methods with and without CSF using

BayesShrink adaptive threshold for images corrupted with Gaussian noisehaving 2 = 0.03 (a) Original LENA image, (b) Noisy LENA image, (c)Output without CSF, (d) Output with CSF, (e) Original PEPPERS image,(f) Noisy PEPPERS image, (g) Output without CSF, (h) Output with CSF.

of CSF shows that BayesShrink gives a better perceptable

image than that of Lee. However, with the implementation

of CSF the blurring effect in the case of Lees thresholding is

removed and the final output has a better PSNR and Q than

that of BayesShrink.

V I. CONCLUSION

This paper compensates for the varying contrast sensitivity

of the HVS to obtain a better denoised output. It is evident

from the experimental results that the 11-weight system out-performs the general 6-weight system by providing a bettermapping of the CSF curve into the different frequency sub-

bands of the image. Also, Lees thresholding algorithm gives

better PSNR than BayesShrink in most cases. Further improve-

ments in the image quality are possible by considering the

masking effects of the HVS or by employing a more complex

HVS model.

REFERENCES

[1] S. G. Chang, M. Vetterli, Spatial adaptive wavelet thresholding for imagedenoising, Proc. of Int. Conf. on Image Processing, pp. 374-377, 1997

[2] S.G. Chang, B. Yu, M. Vetterli, Adaptive wavelet thresholding for imagedenoising and compression IEEE Trans. Image Process, vol. 9, pp. 1532-1546, September 2000.

(a) (b) (c) (d)

(e) (f) (g) (h)

Fig. 8. Comparison of denoising methods with and without CSF usingLees adaptive threshold for images corrupted with Gaussian noise having2 = 0.03 (a) Original LENA image, (b) Noisy LENA image, (c) Outputwithout CSF, (d) Output with CSF, (e) Original PEPPERS image, (f) NoisyPEPPERS image, (g) Output without CSF, (h) Output with CSF.

[3] K. Romberg, H. Choi, R.G. Baraniuk, Bayesian tree-structured imagemodeling using wavelet-domain hidden Markov models, IEEE Trans.

Image Processing, vol. 10, pp. 1056-1068, 2001.[4] P. G. J. Barten, Contrast Sensitivity of the Human Eye and Its Effects

on Image Quality, SPIE, Bellingham, Washington, 1999.[5] M. A. Garcf-Perez, The perceived image: efficient modeling of visual

inhomogeneity, Spatial Vision, pp. 89-99, 1992.[6] M.J. Nadenau, J. Reichel, M. Kunt, Wavelet based color image com-

pression: exploiting the contrast sensitivity function, IEEE Trans. ImageProcessing, vol. 12, pp. 58 - 70, 2003.

[7] A.B. Watson, G.Y. Yang, J.A. Solomon, J. Villasenor, Visual thresholdsfor wavelet quantization error, Proc. of SPIE Conf. on Human Visionand Electronic Imaging, pp. 2657 , 1997.

[8] Z. Wang, A. Bovik, A universal image quality index, IEEE SignalProcess. Lett., vol. 9, pp. 81-84 , 2002.

[9] A.R. Weeks, Fundamentals of Electronic Image Processing, SPIE Optical

Engineering Press and IEEE Press, New York, 1996.[10] G. Sharma, M. Vrehl, H. Trussell, Color image for multimedia, Proc.

of IEEE, vol. 86, pp. 1088-1108, June 1998.[11] I. Daubechies, W Swelden, Factoring wavelet transforms into lifting

steps, Jounal of Fourier Anal. Appl., vol. 4, no. 3, pp. 247-269, 1998.[12] E. Peli, Contrast in complex images, Jounal of Opt. Soc. Am. A, vol.

7, pp. 2032-2040, 1990.[13] W. Schreiber, Fundamentals of Electronic Imaging Systems, Springer,

New York, 1993.[14] S. A. Klein, et al., Seven models of masking, Proc. of SPIE, San Jose,

CA, vol. 3016, pp. 13-24, 1997.[15] Y. H. Lee, S. B. Rhee, Wavelet-based image denoising with optimal

filter, Int. Journal of Information Processing Systems, vol.1, no.1, pp.

32-35, 2005.[16] S. Mallat, Wavelet for a vision, Proc. of IEEE, vol. 84, pp. 604-614,

1996.[17] K. T. Mullen, The contrast sensitivity of human color vision to red-

green and blue-yellow chromatic gratings, Journal of Physiol., vol. 35,pp. 281-400, 1985.

501

color image denoising in wavelet domain using adaptive thresholding incorporating the human visual...

Documents