Redundant Multiscale Transforms and Their Application for Morphological Component Separation

By Jean-Luc Starck, Michael Elad, David L. Donoho. 2004

431 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/f7ea3fe2ed857119c2c9614a5d07521fb7b7bf62

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In Computer Vision and Pattern Recognition

In Media Technology

Citations in the corpus

Sparsity- and continuity-promoting seismic image recovery with curvelet frames (2008, methodology): “The above nonlinear optimization problem (P� ) is solved with a cooling method (see, e.g., [ 39 ]).”
Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) (2005, methodology): “As can be seen, by replacing the mask matrix by the identity operator we obtain the very same algorithm as proposed in [25, 26 ] for the task of image decomposition.”
Inpainting and Zooming Using Sparse Representations (2009, methodology): “This algorithm is a direct extension of the MCA (Morphological Component Analysis), designed for the separation of an image into different semantic components [30, 31 ].”
Non-parametric seismic data recovery with curvelet frames (2008, methodology): “If after these iterations the condition ‖y −Ax̃λ‖2 ≤ is not met, the Lagrange multiplier is lowered and the previous solution is used as a first guess for the new subproblem (Starck et al., 2004; Elad et al., 2005).”
Sparse Solution Of Underdetermined Linear Equations By Stagewise Orthogonal Matching Pursuit (2006, methodology): “x0 represents the synthesis coecients of a signal is assumed to be sparsely represented from terms in an overcomplete expansion; those terms are the columns of . The sparsity allows to recover a unique representation using only a few terms, despite the fact that representation is in general nonuniqu”
Why Simple Shrinkage Is Still Relevant for Redundant Representations? (2006, methodology): “We intend to minimize f(x) = 1 2 kx yk22 + 1 T fWxg: (2) In our notations, ( ) is an arbitrary scalar function.”
Morphological Component Analysis: An Adaptive Thresholding Strategy (2007, background): “In practice, hard thresholding leads generally to better results [ 1 ], [2].”
The Undecimated Wavelet Decomposition and its Reconstruction (2007, methodology): “A full description of MCA is given in [ 10 ].”
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal (2008, methodology): “slices . Different digital ridgelet transforms can be derived depending on the choice of both the radon algorithm and the wavelet decomposition [ 46 ].”
Optimally Tuned Iterative Reconstruction Algorithms for Compressed Sensing (2009, methodology): “Hence, there is widespread interest in finding fast algorithms that work essentially as well; in particular application work by Starck and coauthors [ 13 ], [14], [32], [35], and by Elad and coauthors [15], [17] has shown that some very simple iterative algorithms can be strikingly successful on ver”
Cluster-formation in the Rosette molecular cloud at the junctions of filaments (2012, neutral): “Figure 1 (left) shows a curvelet image from a multi-resolutin morphological decomposition (Starck et al. 2004) of the column density map of the Rosette (see Fig.”
Fast Discrete Curvelet Transforms (2006, background): “Soon after their introduction, researchers developed numerical algorithms for their implementation [37, 18], and scientists have started to report on a series of practical successes, see [ 39 , 38, 27, 26, 20] for example.”
Enhancing Sparsity by Reweighted ℓ1 Minimization (2007, background): “When � is redundant, (18) involves fewer unknowns than (17) and may be computationally simpler to solve [ 53 ].”
Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse (2008, methodology): “In the belief that true ‘1 minimization is far too slow for large-scale applications, numerous authors have explored approximate algorithms based on iterative thresholding or similar ideas; examples include [23, 11, 48, 49 , 25]; related ideas include projection onto convex sets [6].”