Robust Smoothing of Quantitative Genomic Data Using Second-Generation Wavelets and Bivariate Shrinkage

Recent high-throughput nucleotide sequencing technologies provide large amounts of quantitative genomic data, and thus, biologists currently need to process vast quantities of the data on a regular basis. The first step of the process is almost always smoothing of the data because biomedical data generally tend to contain a lot of noise. In this first step, classical wavelet transforms are widely used; however, the second-generation wavelet transform has not been used in biomedical studies. Smoothing based on the second-generation wavelets is more effective than classical wavelets-based methods because it employs data-dependent wavelet functions and does not require predefined explicit base functions. Since biomedical data usually lack regularity, it is more useful in biomedical research to use the second-generation wavelets than to use the classical wavelets. Therefore, we propose a novel smoothing method based on the second-generation wavelets and bivariate shrinkage, which enables to determine robust thresholds for wavelet-based smoothing, and apply it to synthetic and real genomic data. Experimental results demonstrate the effectiveness of the proposed method.