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Showing posts from April, 2016

Trainlets: cropped wavelet decomposition for high-dimensional learning

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It's being a lonng time: element 120 from the aperiodic table of wavelets is the trainlet, from Jeremias Sulam, Student Member, Boaz Ophir, Michael Zibulevsky, and Michael Elad,  Trainlets: Dictionary Learning in High Dimensions : Abstract: Sparse representations has shown to be a very powerful model for real world signals, and has enabled the development of applications with notable performance. Combined with the ability to learn a dictionary from signal examples, sparsity-inspired algorithms are often achieving state-of-the-art results in a wide variety of tasks. Yet, these methods have traditionally been restricted to small dimensions mainly due to the computational constraints that the dictionary learning problem entails. In the context of image processing, this implies handling small image patches. In this work we show how to efficiently handle bigger dimensions and go beyond the small patches in sparsity-based signal and image processing methods. We build our approach bas

M-band 2D dual-tree (Hilbert) wavelet multicomponent image denoising

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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: 4-band directional dual-tree wavelets The set of wavelet functions implements: several dual-tree M-band wavelet tra