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The Undecimated Wavelet Decomposition and its Reconstruction
TLDR
We have shown in this paper that reconstruction from undecimated wavelet transform coefficients can be addressed in a very different way compared to the usual one. Expand
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Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal
TLDR
In order to denoise Poisson count data, we introduce a variance stabilizing transform applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant variance. Expand
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Fractional Gaussian noise, functional MRI and Alzheimer's disease
TLDR
We show that there are significant differences between patients with early Alzheimer's disease (AD) and age-matched comparison subjects in the persistence of fGn in the medial and lateral temporal lobes, insula, dorsal cingulate/medial premotor cortex and left pre- and postcentral gyrus: patients with AD had greater persistence of resting fMRI noise (larger H) in these regions. Expand
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A Generalized Forward-Backward Splitting
TLDR
This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$'s are simple in the sense that their Moreau proximity operators are easy to compute. Expand
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Morphological Component Analysis: An Adaptive Thresholding Strategy
TLDR
In a recent paper, a method called morphological component analysis (MCA) has been proposed to separate the texture from the natural part in images. Expand
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Sparsity and Morphological Diversity in Blind Source Separation
TLDR
This paper introduces a new BSS method coined generalized morphological component analysis (GMCA) that takes advantages of both morphological diversity and sparsity, using recent sparse overcomplete or redundant signal representations. Expand
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Inpainting and Zooming Using Sparse Representations
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We introduce an expectation maximization-based iterative algorithm for image inpainting and interpolation based on sparse representations. Expand
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Dequantizing Compressed Sensing: When Oversampling and Non-Gaussian Constraints Combine
TLDR
In this paper, we study the problem of recovering sparse or compressible signals from uniformly quantized measurements. Expand
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Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
TLDR
We propose a method composed of several stages: we use the log-image data and apply a reasonable under-optimal hard-thresholding on its curvelet transform; then we apply a variational method where we minimize a specialized hybrid criterion composed of an ℓ1 data-fidelity to the thresholded coefficients and a Total Variation regularization (TV) term. Expand
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Image Decomposition and Separation Using Sparse Representations: An Overview
TLDR
This paper gives essential insights into the use of sparsity and morphological diversity in image decomposition and source separation by reviewing our recent work in this field. Expand
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