Numerical performance of block thresholded wavelet estimators
Statistics and Computing
Empirical Bayes approach to block wavelet function estimation
Computational Statistics & Data Analysis
A Nonlinear Stein-Based Estimator for Multichannel Image Denoising
IEEE Transactions on Signal Processing - Part II
Embedded image coding using zerotrees of wavelet coefficients
IEEE Transactions on Signal Processing
Singularity detection and processing with wavelets
IEEE Transactions on Information Theory - Part 2
De-noising by soft-thresholding
IEEE Transactions on Information Theory
A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising
IEEE Transactions on Image Processing
Image denoising using scale mixtures of Gaussians in the wavelet domain
IEEE Transactions on Image Processing
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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.