Systholic Boolean Orthonormalizer Network in Wavelet Domain for Microarray Denoising
Authors: Mario Mastriani
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1073136Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1177
 E.C. Rouchka. (2004, April). Lecture 12: Microarray Image Analysis. (Online). Available: http://kbrin.a-bldg.louisville.edu/ CECS694/Lecture12.ppt
 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
 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
 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.
 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.
 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.
 X.-P. Zhang, "Thresholding Neural Network for Adaptive Noise reduction," IEEE Trans. on Neural Networks, vol.12, no. 3, pp.567- 584, May 2001.
 I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
 B.B. Hubbard, The World According to Wavelets: The Story of a Mathematical Technique in the Making, A. K. Peter Wellesley, Massachusetts, 1996.
 S. G. Mallat, "Multiresolution approximations and wavelet orthonormal bases of L2 (R)," Transactions of the American Mathematical Society, 315(1), pp.69-87, 1989a.
 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.
 C. Valens. (2004). A really friendly guide to wavelets. (Online). Available:http://perso.wanadoo.fr/polyvalens/ clemens/wavelets/wavelets.html
 G. Kaiser, A Friendly Guide To Wavelets, Boston:Birkhauser, 1994.
 I. Daubechies, "Different Perspectives on Wavelets," in Proceedings of Symposia in Applied Mathematics, vol. 47, American Mathematical Society, USA, 1993.
 J. S. Walker, A Primer on Wavelets and their Scientific Applications, Chapman & Hall/CRC, New York, 1999.
 E. J. Stollnitz, T.D. DeRose, and D.H. Salesin, Wavelets for Computer Graphics: Theory and Applications, Morgan Kaufmann Publishers, San Francisco, 1996.
 J. Shen and G. Strang, "The zeros of the Daubechies polynomials," in Proc. American Mathematical Society, 1996.
 A.K. Jain, Fundamentals of Digital Image Processing, Englewood Cliffs, New Jersey, 1989.
 M. Mastriani, "Enhanced Boolean Correlation Matriz Memory", (RNL02), in Proceedings of X RPIC Reuni├│n de Trabajo en Procesamiento de la Informaci├│n y Control, San Nicol├ís, Buenos Aires, Argentina, October 8-10, 2003.
 G. Delfino and F. Martinez. (2000, March). Watermarking insertion in digital images (spanish). (Online). Available: http://www.internet.com.uy/fabianm/watermarking.pdf
 Y. Yu, and S.T. Acton, "Speckle Reducing Anisotropic Diffusion," IEEE Trans. on Image Processing, vol. 11, no. 11, pp.1260-1270, 2002.
 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