Noise reduction for enhanced component identification in multi-dimensional biomolecular NMR studies

The objective of the research presented in this paper is to shed light into the benefits of multi-dimensional wavelet-based methodology applied to NMR biomolecular data analysis. Specifically, the emphasis is on noise reduction for enhanced component identification in multi-dimensional mixture regression. The contributions of this research are multi-fold. First, the wavelet-based noise reduction method applies to multi-dimensional data whereas most of the existing work focuses on one- or two-dimensional data only. The proposed wavelet-based methodology is founded on rigorous analysis of the dependence between wavelet coefficients, an important aspect of multi-dimensional wavelet de-noising. The wavelet de-noising rule is based on Stein's unbiased risk estimator (SURE) where the smoothness thresholds vary with the resolution level and orientation of the wavelet transform and selected by controlling the False Discovery Rate of the significant wavelet coefficients. Second, this paper highlights the application of the wavelet methodology to multi-dimensional NMR data analysis for protein structure determination. The noise reduction method is general and applicable to multi-dimensional data arising in many other research fields, prominently in biology science. Our empirical investigation shows that reducing the noise using the method in this paper results in more detectable true components and fewer false positives without altering the shape of the significant components.