Study and Analysis of Microarray Denoising using Systholic Boolean Orthonormalizer Network in Wavelet Domain

In this paper, we present a new approach to deal with the noise inherent in the microarray image processing procedure. 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. Southern Detection of specific sequences among DNA fragments separated by gel electrophoresis. , 1975, Journal of molecular biology.

[2]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[3]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  S. Mallat Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[5]  I. Johnstone,et al.  Adapting to Unknown Smoothness via Wavelet Shrinkage , 1995 .

[6]  David Salesin,et al.  Wavelets for computer graphics: theory and applications , 1996 .

[7]  Barbara Burke Hubbard The World According to Wavelets: The Story of a Mathematical Technique in the Making, Second Edition , 1996 .

[8]  Hervé Carfantan,et al.  Time-invariant orthonormal wavelet representations , 1996, IEEE Trans. Signal Process..

[9]  C. Valens,et al.  A Really Friendly Guide to Wavelets , 1999 .

[10]  Martin Vetterli,et al.  Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..

[11]  Robert Clarke,et al.  Iterative normalization of cDNA microarray data , 2002, IEEE Transactions on Information Technology in Biomedicine.

[12]  R.S.H. Istepanian,et al.  Microarray image enhancement by denoising using stationary wavelet transform , 2003, IEEE Transactions on NanoBioscience.

[13]  Y. H. Song,et al.  Microarray image de-noising using stationary wavelet transform , 2003, 4th International IEEE EMBS Special Topic Conference on Information Technology Applications in Biomedicine, 2003..

[14]  Donald A. Adjeroh,et al.  On denoising and compression of DNA microarray images , 2006, Pattern Recognit..

[15]  C. Burrus,et al.  Speckle Reduction via Wavelet Shrinkage with Application to SAR based ATD/R , 2009 .

[16]  Mario Mastriani,et al.  Enhanced Directional Smoothing Algorithm for Edge-Preserving Smoothing of Synthetic-Aperture Radar Images , 2016, ArXiv.

[17]  Ingrid Daubechies Different Perspectives on Wavelets , 2016 .