Proceedings of the Second APSIPA Annual Summit and Conference, pages 387–392,Biopolis, Singapore, 14-17 December 2010.

Approaches based on non-separable filter banks in 2D Gel electrophoresis image analysis

Ratnesh Singh Sengar*, A.K.Upadhyay*, Pushkar G. Patwardhan†, Manjit Singh* and V. M.Gadre†

*Division of Remote Handling & Robotics, Bhabha Atomic Research Centre, Mumbai, India-400085 E-mail: rssengar@barc.gov.in Tel/Fax: +91-22-2559-2139/+91-22-25505363

†Department of Electrical Engineering, Indian Institute of Technolgy Bombay,Mumbai, India-400076 E-mail: vmgadre@ee.iitb.ac.in Tel/Fax: +91-22-2576-7426 / +91-22-2572-3707

Abstract— Analysis and interpretation of 2D gel images is a very important task in proteonomics study. The nonlinearties in the gel formation and image acquisition process leads to distortions, overlapped protein spots, saturated spots, faint spots, nonlinear intensity and uneven background in the gel images. As a result, pre-processing steps are important before image-analysis. De-noising is one of the most important pre-processing steps, and the overall accuracy of protein spot detection and analysis depends crucially on how effectively the 2D gel images have been de-noised. Non-separable processing methods, due to their inherent ability to be able to better represent directional information, seem to be promising for the processing of 2D gel images. In this paper, we explore approaches based on quincunx non-separable filter-banks for image de-noising, and show the overall effect on the protein spot detection accuracy.

I. INTRODUCTION

Two dimensional electrophoresis is an important technique for analyzing protein expression and for enhancing data quality in the field of proteomics. Proteomics is the field that studies a multi-protein system, focusing on the interplay of multiple proteins as functional components in a biological system. By this technique a very large number of proteins can easily and simultaneously be separated, identified and characterized. This is important for understanding protein function and thus enables the development of new and more effective drugs [2].

The first step in a typical proteomics analysis workflow is proteins separation, followed by quantification and differential expression analysis. Despite its limitations, 2D gel electrophoresis (2DGE) remains the most widely used protein separation method. Using 2DGE, individual proteins in a mixture are resolved in the first gel dimension according to their molecular weight and in the second dimension according to their isoelectric point [1] [4].

A very important task in a proteomics study is the correct analysis and interpretation of 2D gel images through image analysis. The objective is to extract the protein spots in gel images from the uneven background which has sharp edges, e.g... lines, artifacts and streaks in some area. Many authors report the experience typified in the following description: Due to some technical problems such as the system nonlinearities in gel formation and image acquisition, inevitably there appear overlapped protein spots, saturated

spots, faint spots, nonlinear intensity and narrow lines on the gels which make the task more difficult [3][4].

The noise suppression methods used in commercially available image analysis software packages are based on spatial filtering. Despite their simplicity, these filters tend to severely distort spot edges and alter the intensity values of spot pixels. This is not surprising since 2DGE images are typical examples of signals with rapidly varying local character, due to the large and unstructured variations in spot intensities and size. It is impossible to distinguish 'signal' from 'noise' in the space or frequency domain alone. It is therefore appropriate to use a joint domain.

We employ a Wavelet Transform (WT) [8] that outperforms spatial filtering, both in terms of Peak Signal to Noise Ratio (PSNR) and in terms of minimizing spot edge distortions. As 2-D wavelet transforms extensively focus on the three directions (vertical, horizontal and diagonal), an enormous amount of singular information in other directions cannot be revealed in the high frequency component. Hence quincunx non-separable wavelets and filter banks find a good potential application here. One well known discrete non-separable wavelet transform, comprises of the filter banks, which are constructed by using centrally symmetric orthogonal matrices. Even though this is a non-separable transform, the computational complexity is not significantly greater while maintaining a more general form of multiresolution character. Our investigation demonstrates that the high frequency components from this non-separable WT can capture more singular information than traditional wavelets. Therefore, it motivates us to apply an approach based on the non-separable wavelet to extract the features of 2D Gel electrophoresis images. We have evaluated the relative performance of separable and non-separable wavelet approaches independently in this paper and found our results to be at some variance with the results of Tsakanikas and Manolokos [17]. The common observation has been, though, that non-separable wavelets have a good case which these authors exemplify by using contourlets [18] for de-noising of gel images and we exemplify by using the quincunx filter bank.

II. NON-SEPARABLE WAVELET QUINCUNX

387

10-0103870392©2010 APSIPA. All rights reserved.

In the context of wavelets and filter-banks, non-separable systems have non-rectangular frequency supports for the subbands in subbands, thus resulting in better frequency selectivity. The simplest decomposition of that type, known as the Quincunx transform (QT), uses non-separable and non-oriented filters, followed by the non-separable sampling represented by the matrix Dq in (1) below. The Quincunx lowpass and highpass filters are often chosen to have diamond shaped frequency supports, as shown in Fig-1 below. With these diamond shaped frequency responses, the lowpass filter can preserve the high frequencies in the vertical and horizontal directions, which is a good match to the human visual system since the visual sensitivity is higher to changes in these two directions than the other directions. Due to this, Quincunx filter banks are particularly important in image processing applications.

Since the det Dq=2, this transform is performed with a two-

channel filter bank. At each level, the input image is decomposed with the multiresolution scale factor 2, resulting in one low-resolution subimage and one non-oriented wavelet subimage.

Dq = ⎥⎦

⎤⎢⎣

⎡− 11

11

A quincunx filter bank has the canonical form shown in Fig2.

Fig. 2 Canonical form of Quincunx filter bank The filter bank consists of low pass and high pass analysis filters H0 and H1, low pass and high pass synthesis filters G0 and G1, and M-fold down samplers and up samplers. Instead of using the standard canonical polyphase structure, the lifting factorization is often more convenient to design and implement the Quincunx filter bank [12]. The lifting structure guarantees Perfect Reconstruction (PR), and the

so-called predict and update lifting steps can be used to increase the order of the polyphase matrix (and thus of the filters) while maintaining PR. The predict and update steps ( )(P z and )(U z respectively) involve factorizing the analysis polyphase matrix in factors of the following form:

⎥⎦

⎤⎢⎣

⎡−⎥

⎦

⎤⎢⎣

⎡=

1)(P01

10)(U1

'z

z)(E z

The corresponding synthesis matrix is given by

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=

10)(U-1

1)(P01

'z

z)(zR

It is easy to see that this filter bank is PR by construction, regardless of the specific choice of the update or predict steps )(U z or )(P z .

By using multiple such update and predict steps, with different )(P z and )(U z functions, a Quincunx filter bank with higher order filters can be constructed. The lifting realization of a quincunx filter bank has the form shown in Fig. 3.

Fig. 3 Lifting Schme of Quincunx filter bank. (a) Analysis (b) Synthesis

Essentially, the filter bank is realized in polyphase form,

with the analysis and synthesis polyphase filtering each being performed by a ladder network consisting of 2λ lifting filters {Ak}. Due to the use of the lifting framework, the PR condition is automatically satisfied. The main feature of lifting is that it allows us to satisfy three properties of the filter bank separately: 1) PR: Perfect reconstruction property 2) DM: Dual vanishing moments 3) PM: Primal vanishing moments [14].

We have used quincunx interpolating filter banks designed by Kovacevic and Sweldens [14], based on the lifting scheme [12].The quincunx filter banks have truly non-separable wavelet decomposition, contrary to non-separable wavelets biased in horizontal and vertical directions.

Since the decimated transform is not shift invariant, the de-noising result will depend on the position of the discontinuities in the image. Undecimated versions of wavelet transforms are often seen to give better results [7]. In this paper, we use undecimated version only, so we remove the decimation operator from the quincunx lifting

(1)

H0

H2

H1

ππ ,

ππ ,--

ππ ,-

ππ ,-

ππ ,

ππ ,--

ππ ,-

ππ ,-

0ω

1ω

0ω

1ω

Fig. 1 Frequency supports of filters in Quincunx filter-bank

388

scheme [14] and the N-times quincunx upsampled versions of {Ak} filters are used, where N represents decomposition level. This way for higher decomposition levels the corresponding filter support widens.

III. DE-NOISING METHOD AND THRESHOLD CRITERION

Electrophoresis images can be considered as signals with many sharp features or signals containing features in a variety of frequency bands. Efficient elimination of noise, without deteriorating the significant high frequency features, can be performed in the wavelet domain (e.g. [7][9][10][11][13][15][16]). In the case of such a signal, it is impossible to distinguish between the signal and the noise component in the time domain, whereas it is possible in the time-frequency (wavelet) domain. This approach consists in erasing to zero, all the small wavelet coefficients associated with noise, while preserving the wavelet coefficients associated with the high- frequency signal components, such as narrow peaks or spots. This feature of the wavelet filtering allows an effective suppression of noise without erasing the important details in the studied signal. It can be presented as a three-step method: (i) decomposition of the image on the set of the wavelet basis functions (ii) thresholding of the wavelet coefficients and (iii) inverse transformation of the thresholded coefficients into the original domain. Once the image is decomposed, the unimportant or undesired details can be removed by a thresholding technique. There are two types of the thresholding policies (functions) : (i) Hard thresholding: For a particular 'ith' coefficient vi and a threshold value, the thresholded coefficients, are determined as:

{ thresholdvforvthresholdvfor

thi

ii

iv ≥

<= ||||0

i.e., all the coefficients below a threshold value are

discarded (i.e., replaced with zeros). (ii) Soft thresholding: In the soft thresholding (also called

the shrinkage), all coefficients are shrunk towards zero by the threshold value:

{ thresholdvforthresholdvvsignthresholdvfor

thi

iii

iv ≥−

<= ||)|)(|(||0

Hard thresholding can lead to better reproduction of the

peak heights and discontinuities, but at a price, of occasional artifacts that can roughen the appearance of the image estimate [17]. The threshold value can be calculated, using different approaches and it can be applied to the different numbers of wavelet coefficients. Depending on the location of the coefficient the threshold is applied to, there are different kinds of thresholds mainly: (i) global – one threshold value used for all wavelet coefficients; (ii) level-dependent – one threshold value for all the coefficients on a given level of decomposition; The most popular criteria for threshold estimation are the mean-square error (“Risk”

[18]), Stein Unbiased Risk Estimate (“Sure” [11]), and visual quality (“Visu” [17]). According to [4], one of the most effective approaches to denoising the two-dimensional gel images is the so-called Bayes threshold method [13]. In this approach the threshold value is estimated, based on the generalized Gaussian distribution parameters:

is

threshold,

2

σσ

=

Where σ and σs,i are empirically calculated as: σ = 1.4826 median (|v1|) where v1 are the wavelet coefficients from the scale 1, and

)0,max( 22, σσσ −= iis

for i = 1, 2, . . . , L, Where σi

2 denotes the variance of the coefficients from the i-th level, and L denotes the decomposition level. In our study this method of thresholding was applied with a soft-thresolding policy. After thresholding, the inverse wavelet transform is used for image reconstruction.

IV. EVALUATION METHODOLOGY

In our experiment, we have compared the performance of the quincunx wavelet and traditional dyadic wavelets for de-noising of gel images. For a fair comparison, we first find the best set of parameters for traditional separable wavelets for de-noising. This set of parameters consists of basis functions, the number of decomposition levels and the coefficient shrinkage method. The comparative study is performed first in terms of PSNR and then in terms of introduced distortion.

For real gel images, it is impossible to find out image with “ground-truth” known, so noise –free synthetic images are also generated for proper evaluation. Every spot has been modeled using a 2D Gaussian function. Each image has 512 x 512 pixels, 8 bits per pixel and contains a randomly selected number of spots, 10 to 200. Then, we have added white Gaussian noise with standard deviation σ= 5, 10, 15, 20, 30 and 40.

V. EXPERIMENTS, RESULTS AND DISCUSSIONS

In [4], different wavelet bases are compared with each other along with different decomposition levels and the authors point out that the Coiflet, with ten vanishing moments gives better results. It is also found that three decomposition levels are the best for de-noising. We have used the Daubechies, Coiflet and Symlet wavelets with different vanishing moments. Our results match with results presented in [4]. In comparison with other shrinkage methods, the Bayes thresolding [13] method gives better results in our experiment as well as in [4]. Our sets of synthetic images are processed through a Quincunx Transform with 4 vanishing moments and a

(2)

(3)

where i=1,2,…, L

389

Coiflet transform with ten vanishing moments. Table 1 provides the mean PSNR value over all images in our set, when corrupted with one of six noise levels and Fig.4 shows a part of the processed synthetic image. We can observe that for Bayes thresolding and 3 decomposition levels, the Quincunx Transform outperforms the Coiflet approach – as per the explanation to follow herewith. The 3D Profile of original image and filtered images are presented in Fig. 5. One can see, qualitatively, that the image filtered using a Quincunx filter bank contains more edge information and thus causes less distortion to the original image. We have also applied a watershed transform [5][6] on the denoised real gel images as shown in Fig. 6 and found an improved result in the Quincunx method. We have also processed our set of de-noised images through the Delta2D software and

found that the more numbers of true spots are detected and the number of false spots has been reduced in case of the Quincunx filter bank. Fig. 7 shows the result obtained on using the Delta2D software for a real gel image.

(a) (b) (c)

Fig. 4 A part of synthetic image is shown.(a) synthetic image with introduced noise (b) image de-noised using coiflet wavelet (c) image de-noised using quincunx wavelet.

(a) Original image (b) Noisy image

(c) De-noised with coiflet (d) De-noised with quincunx

Fig. 5 3D view of images.

TABLE I MEAN PSNR VALUES FOR OUR SET OF SYNTHETIC IMAGES WITH

INTRODUCED NOISE LEVELS σ Noisy image Coiflet qunicunx 5 23.006 30.429 30.816 10 19.110 27.201 27.001 15 18.964 24.756 26.583 20 17.491 24.510 24.629 30 17.468 23.641 24.569

390

VI. CONCLUSIONS AND FUTURE WORK

In this paper, we have used a shift invariant Quincunx wavelet for de-noising of 2Dgel images. To the best of our knowledge, it is first attempt to compare the performance of the Quincunx filter bank with a separable wavelet approach for 2DE gel images. We have found that the Quincunx approach has performed as well or better than the Coiflet for our set of gel images. Since de-noising is very critical part for segmentation of gel image, even a small improvement in this step has a very positive effect. Lifting scheme enables parallel, in place and faster computation of non-separable quincunx transform. Future work will concentrate on designing other non-separable filters and improvement in the Quincunx filter bank using lifting scheme, to get better

results.We shall also explore other non-separable approaches for multiplicative and impulsive noise removal.

REFERENCES

[1] P.H. O’Farrell, ‘High resolution two-dimensional gel electrophoresis of proteins,” J.Biological Chem., vol.250,pp.4007-4021,1975.

[2] L.Anderson and N.Anderson, “Some perspectives on two-dimensional protein mapping,” Clinical Chemistry, vol.30, pp.1898-1905,Dec.1984.

[3] Pierre Marie Nugues, “Two-Dimensional Electrophoresis Image Interpretation,” IEEE Trans. On Biomedical Engineering, Vol.40, No.8., August1993.

(a) Original Gel Image (b) De-noised using coiflet (c) De-noised using quincunx

Fig. 6 Original and de-noised gel images.

(a) (b)

Fig. 7 . De-noised images are processed through Delta 2D package. Segmented images are shown. (a) image denoised by coiflet and processed. Total 412 spots are detected. (b) image denoised by quincunx and processed. Total 446 spots are detected.

391

[4] K.Kaczmarek et al, “Preprocessing of two-dimensional gel electrophoresis images,”Proteomics 2004 vol.4, pp.2377-2389

[5] Victor Osma-Ruiz, Juan I. Godino-LIorente, Nicolas Saenz-Lechon, Pedro Gomez-Vilda, “An Improved watershed algorithm based on efficient computation of shortest paths,”Elsevier on Pattern Recognition 40(2007) 1078-1090.

[6] L.Vincent and P.Soille, “Watershed in digital spaces: An efficient algorithm based on immersion simulations,” IEEE Trans. On Pattern Analysis and Machine Intelligence, Vol.13, no.6, pp. 583-598, June 1991

[7] R.Coifman and D. Donoho, “Translation-invariant Denoising,” in Wavelets and Statistics, A Antoniadis and G. Oppenheim (eds.), Springer-Verlag,pp.125-150,1995.

[8] S. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence11, pp. 674–693, July 1989.

[9] J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image Denoising using Scale Mixtures of Gaussians in the Wavelet Domain,” IEEE Transactions on Image Processing 12, pp. 1338–1351, November 2003.

[10] A. Piˇzurica and W. Philips, “Estimating the Probability of the Presence of a Signal of Interest in Multiresolution Single- and Multiband Image Denoising,” IEEE Transactions on Image Processing 15, pp. 654–665, March 2006.

[11] F. Luisier, T. Blu, and M. Unser, “A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding,” IEEE Transactions on Image Processing 16, pp. 593–606, March 2007.

[12] W.Sweldens, “The lifting scheme: A custom-design construction of bioorthogonal wavelets,” Applied and Computational Harmonic Analysis, vol.3,pp.186-200,1996.

[13] F. F. Abramovich, T. Sapatinas, and B. Silverman,”Wavelet thresholding via a Bayesian approach,” J. Royal Statistical Society, 1998, vol. 60, pp. 725-749.

[14] Jelena Kovacevic and Wim Sweldens, “Wavelet Families of Increasing Order in Arbitrary Dimensions,” IEEE Transactions on Image Processing 9(3), pp. 480-496, March 2000.

[15] Kwan-Deok Choi, Mi-Ae Kim and Young-Woo Yoon, “Adaptive thresholding for eliminating noises in 2-DE image,” Journal of Signal Processing and Systems, 9, 1-9,2008.

[16] M.Dasykowski, I.Stanimirova, A.Bodzon-Kulakowska et al , “Start-to-end processing of two-dimensional gel electrophoretic images,” Elsevier on Chromatography A 1158(2007) 306-317.

[17] P.Tsakanikas and I.Manolakos “Effective denoising of 2D Gel proteomics images using contourlets”, IEEE International Conference on Image Processing, 2007, vol.6, pp.269-272, 2007.

[18] Minh N.Do and Martin Vetterli, “The Contourlet Transform: An Efficient Directional Multiresolution Image Representation,” IEEE Trans. On Image Processing, vol.14, pp. 2091-2106, 2005.

392