The toolbox implements a parametric nonlinear estimator that generalizes several wavelet shrinkage denoising methods. Dedicated to additive Gaussian noise, it adopts a multivariate statistical approach to take into account both the spatial and the inter-component correlations existing between the different wavelet subbands, using a Stein Unbiased Risk Estimator (SURE) principle, which derives optimal parameters. The wavelet choice is a slightly redundant multi-band geometrical dual-wavelet frame. Experiments on multispectral remote sensing images outperform conventional wavelet denoising techniques (including curvelets).
The set of functions implements:
* several dual-tree M-band wavelet transforms from: Image analysis using a dual-tree M-band wavelet transform, IEEE TRANSACTIONS ON IMAGE PROCESSING, 2006, http://dx.doi.org/10.1109/TIP.2006.875178
* a neighborhood choice from: Noise covariance properties in dual-tree wavelet decompositions, IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, http://dx.doi.org/10.1109/TIT.2007.909104
* the non-linear Stein estimator: A nonlinear Stein-based estimator for multichannel image denoising, IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2008, http://dx.doi.org/10.1109/TSP.2008.921757
* relative merits of different directional 2D wavelets are detailed in: A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity, SIGNAL PROCESSING, 2011, http://dx.doi.org/10.1016/j.sigpro.2011.04.025
The demonstration script is Init_Demo.m, and the functions for M-band dual-tree wavelets are provided in the directory TOOLBOX_DTMband_solo
Laurent Duval (2022). M-band 2D dual-tree (Hilbert) wavelet multicomponent image denoising (https://www.mathworks.com/matlabcentral/fileexchange/56705-m-band-2d-dual-tree-hilbert-wavelet-multicomponent-image-denoising), MATLAB Central File Exchange. Retrieved .
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