Systholic Boolean Orthonormalizer Network in Wavelet Domain for Microarray Denoising
We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT-2D) to the Noisy Microarray, 2) scaling and rounding to the coefficients of the highest subbands (to obtain integer and positive coefficients), 3) bit-slicing to the new highest subbands (to obtain bit-planes), 4) then we apply the Systholic Boolean Orthonormalizer Network (SBON) to the input bit-plane set and we obtain two orthonormal otput bit-plane sets (in a Boolean sense), we project a set on the other one, by means of an AND operation, and then, 5) we apply re-assembling, and, 6) rescaling. Finally, 7) we apply Inverse DWT-2D and reconstruct a microarray from the modified wavelet coefficients. Denoising results compare favorably to the most of methods in use at the moment.
[1] E.C. Rouchka. (2004, April). Lecture 12: Microarray Image
Analysis. (Online). Available: http://kbrin.a-bldg.louisville.edu/
CECS694/Lecture12.ppt
[2] X.H. Wang, S.H. Istepanian, and Y.H. Song, "Microarray Image
Enhancement by Denoi-sing Using Stationary Wavelet Transform,"
IEEE Transactions on Nanobioscience, vol.2, no. 4, pp.184-189,
December 2003. (Online). Available:
http://technology.kingston.ac.uk/
momed/papers/IEEE_TN_Micorarray_Wavelet%20Denoising.pdf
[3] H.S. Tan. (2001, October). Denoising of Noise Speckle in Radar
Image. (Online). Available:
http://innovexpo.itee.uq.edu.au/2001/projects/s804294/thesis.pdf
[4] H. Guo, J.E. Odegard, M. Lang, R.A. Gopinath, I. Selesnick, and
C.S. Burrus, "Speckle reduction via wavelet shrinkage with
application to SAR based ATD/R," Technical Report CML TR94-
02, CML, Rice University, Houston, 1994.
[5] D.L. Donoho and I.M. Johnstone, "Adapting to unknown
smoothness via wavelet shrinkage," Journal of the American
Statistical Association, vol. 90, no. 432, pp. 1200-1224, 1995.
[6] S.G. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding
for image denoising and compression," IEEE Transactions on Image
Processing, vol. 9, no. 9, pp.1532-1546, September 2000.
[7] X.-P. Zhang, "Thresholding Neural Network for Adaptive Noise
reduction," IEEE Trans. on Neural Networks, vol.12, no. 3, pp.567-
584, May 2001.
[8] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
[9] B.B. Hubbard, The World According to Wavelets: The Story of a
Mathematical Technique in the Making, A. K. Peter Wellesley,
Massachusetts, 1996.
[10] S. G. Mallat, "Multiresolution approximations and wavelet
orthonormal bases of L2 (R)," Transactions of the American
Mathematical Society, 315(1), pp.69-87, 1989a.
[11] A. Grossman and J. Morlet, "Decomposition of Hardy Functions
into Square Integrable Wavelets of Constant Shape," SIAM J. App
Math, 15: pp.723-736, 1984.
[12] C. Valens. (2004). A really friendly guide to wavelets. (Online).
Available:http://perso.wanadoo.fr/polyvalens/
clemens/wavelets/wavelets.html
[13] G. Kaiser, A Friendly Guide To Wavelets, Boston:Birkhauser, 1994.
[14] I. Daubechies, "Different Perspectives on Wavelets," in Proceedings
of Symposia in Applied Mathematics, vol. 47, American
Mathematical Society, USA, 1993.
[15] J. S. Walker, A Primer on Wavelets and their Scientific Applications,
Chapman & Hall/CRC, New York, 1999.
[16] E. J. Stollnitz, T.D. DeRose, and D.H. Salesin, Wavelets for
Computer Graphics: Theory and Applications, Morgan Kaufmann
Publishers, San Francisco, 1996.
[17] J. Shen and G. Strang, "The zeros of the Daubechies polynomials,"
in Proc. American Mathematical Society, 1996.
[18] A.K. Jain, Fundamentals of Digital Image Processing, Englewood
Cliffs, New Jersey, 1989.
[19] M. Mastriani, "Enhanced Boolean Correlation Matriz Memory",
(RNL02), in Proceedings of X RPIC Reuni├│n de Trabajo en
Procesamiento de la Información y Control, San Nicolás, Buenos
Aires, Argentina, October 8-10, 2003.
[20] G. Delfino and F. Martinez. (2000, March). Watermarking insertion
in digital images (spanish). (Online). Available:
http://www.internet.com.uy/fabianm/watermarking.pdf
[21] Y. Yu, and S.T. Acton, "Speckle Reducing Anisotropic Diffusion,"
IEEE Trans. on Image Processing, vol. 11, no. 11, pp.1260-1270,
2002.
[22] M. Mastriani and A. Giraldez, "Enhanced Directional Smoothing
Algorithm for Edge-Preserving Smoothing of Synthetic-Aperture
Radar Images," Journal of Measurement Science Review, vol 4, no.
3, pp.1-11, 2004. (Online). Available:
http://www.measurement.sk/2004/S3/Mastriani.pdf
[1] E.C. Rouchka. (2004, April). Lecture 12: Microarray Image
Analysis. (Online). Available: http://kbrin.a-bldg.louisville.edu/
CECS694/Lecture12.ppt
[2] X.H. Wang, S.H. Istepanian, and Y.H. Song, "Microarray Image
Enhancement by Denoi-sing Using Stationary Wavelet Transform,"
IEEE Transactions on Nanobioscience, vol.2, no. 4, pp.184-189,
December 2003. (Online). Available:
http://technology.kingston.ac.uk/
momed/papers/IEEE_TN_Micorarray_Wavelet%20Denoising.pdf
[3] H.S. Tan. (2001, October). Denoising of Noise Speckle in Radar
Image. (Online). Available:
http://innovexpo.itee.uq.edu.au/2001/projects/s804294/thesis.pdf
[4] H. Guo, J.E. Odegard, M. Lang, R.A. Gopinath, I. Selesnick, and
C.S. Burrus, "Speckle reduction via wavelet shrinkage with
application to SAR based ATD/R," Technical Report CML TR94-
02, CML, Rice University, Houston, 1994.
[5] D.L. Donoho and I.M. Johnstone, "Adapting to unknown
smoothness via wavelet shrinkage," Journal of the American
Statistical Association, vol. 90, no. 432, pp. 1200-1224, 1995.
[6] S.G. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding
for image denoising and compression," IEEE Transactions on Image
Processing, vol. 9, no. 9, pp.1532-1546, September 2000.
[7] X.-P. Zhang, "Thresholding Neural Network for Adaptive Noise
reduction," IEEE Trans. on Neural Networks, vol.12, no. 3, pp.567-
584, May 2001.
[8] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
[9] B.B. Hubbard, The World According to Wavelets: The Story of a
Mathematical Technique in the Making, A. K. Peter Wellesley,
Massachusetts, 1996.
[10] S. G. Mallat, "Multiresolution approximations and wavelet
orthonormal bases of L2 (R)," Transactions of the American
Mathematical Society, 315(1), pp.69-87, 1989a.
[11] A. Grossman and J. Morlet, "Decomposition of Hardy Functions
into Square Integrable Wavelets of Constant Shape," SIAM J. App
Math, 15: pp.723-736, 1984.
[12] C. Valens. (2004). A really friendly guide to wavelets. (Online).
Available:http://perso.wanadoo.fr/polyvalens/
clemens/wavelets/wavelets.html
[13] G. Kaiser, A Friendly Guide To Wavelets, Boston:Birkhauser, 1994.
[14] I. Daubechies, "Different Perspectives on Wavelets," in Proceedings
of Symposia in Applied Mathematics, vol. 47, American
Mathematical Society, USA, 1993.
[15] J. S. Walker, A Primer on Wavelets and their Scientific Applications,
Chapman & Hall/CRC, New York, 1999.
[16] E. J. Stollnitz, T.D. DeRose, and D.H. Salesin, Wavelets for
Computer Graphics: Theory and Applications, Morgan Kaufmann
Publishers, San Francisco, 1996.
[17] J. Shen and G. Strang, "The zeros of the Daubechies polynomials,"
in Proc. American Mathematical Society, 1996.
[18] A.K. Jain, Fundamentals of Digital Image Processing, Englewood
Cliffs, New Jersey, 1989.
[19] M. Mastriani, "Enhanced Boolean Correlation Matriz Memory",
(RNL02), in Proceedings of X RPIC Reuni├│n de Trabajo en
Procesamiento de la Información y Control, San Nicolás, Buenos
Aires, Argentina, October 8-10, 2003.
[20] G. Delfino and F. Martinez. (2000, March). Watermarking insertion
in digital images (spanish). (Online). Available:
http://www.internet.com.uy/fabianm/watermarking.pdf
[21] Y. Yu, and S.T. Acton, "Speckle Reducing Anisotropic Diffusion,"
IEEE Trans. on Image Processing, vol. 11, no. 11, pp.1260-1270,
2002.
[22] M. Mastriani and A. Giraldez, "Enhanced Directional Smoothing
Algorithm for Edge-Preserving Smoothing of Synthetic-Aperture
Radar Images," Journal of Measurement Science Review, vol 4, no.
3, pp.1-11, 2004. (Online). Available:
http://www.measurement.sk/2004/S3/Mastriani.pdf
@article{"International Journal of Information, Control and Computer Sciences:58701", author = "Mario Mastriani", title = "Systholic Boolean Orthonormalizer Network in Wavelet Domain for Microarray Denoising", abstract = "We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT-2D) to the Noisy Microarray, 2) scaling and rounding to the coefficients of the highest subbands (to obtain integer and positive coefficients), 3) bit-slicing to the new highest subbands (to obtain bit-planes), 4) then we apply the Systholic Boolean Orthonormalizer Network (SBON) to the input bit-plane set and we obtain two orthonormal otput bit-plane sets (in a Boolean sense), we project a set on the other one, by means of an AND operation, and then, 5) we apply re-assembling, and, 6) rescaling. Finally, 7) we apply Inverse DWT-2D and reconstruct a microarray from the modified wavelet coefficients. Denoising results compare favorably to the most of methods in use at the moment.
", keywords = "Bit-Plane, Boolean Orthonormalization Process,
Denoising, Microarrays, Wavelets", volume = "2", number = "9", pages = "3109-12", }
