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). Since they are based on MIMO filter banks (multi-input, multi-ooutput), in a mullti-band fashion,, we can called they MIMOlets quite safely. The dual-tree wavelet consists in two directional wavelet trees, diisplayed below for a 4-band filter:
The set of wavelet functions implements:
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| 4-band directional dual-tree wavelets |
The set of wavelet 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,
- a neighborhood choice from: Noise covariance properties in dual-tree wavelet decompositions, IEEE TRANSACTIONS ON INFORMATION THEORY, 2007,
- the non-linear Stein estimator: A nonlinear Stein-based estimator for multichannel image denoising, IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2008,
- as a complement, 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,
The (very) noisy version:
The denoised one:
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