Homotopy continuation for sparse signal representation

By Dmitry M. Malioutov, Müjdat Çetin, Alan S. Willsky. Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., 2005

296 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/e9573a8f436da57521dcded69913f355e32cf225

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Citations in the corpus

Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit (2007, background): “OMP is especially efficient when the signal is highly sparse although homotopy methods for (BP) are competitive here [14].”
Fast Solution of $\ell _{1}$ -Norm Minimization Problems When the Solution May Be Sparse (2008, methodology): “[40] were the first to apply the HOMOTOPY method to the formulation in the underdetermined setting, when the data are noisy.”
Handbook of Blind Source Separation: Independent Component Analysis and Applications (2010, methodology): “Algorithms such as LARS (Least Angle Regression) [35] that take more specific account of the optimization problem [105, 35, 74, 85, 45] are able to further simplify and accelerate the calculations.”
Fast L1-Minimization Algorithms For Robust Face Recognition (2010, unknown): “The approach was ﬁrst studied in the context of LASSO [49], which inspired a solution to the forward stagewise linear regression problem called LARS [50] and eventually led to the Homotopy algorithms for basis pursuit in [51], [52].”
Fast ℓ1-minimization algorithms and an application in robust face recognition: A review (2010, background): “in similar conditions as `1-min? In this section, we overview one such approach called homotopy methods [37], [31], [17].”
An Exponential Lower Bound on the Complexity of Regularization Paths (2009, background): “…dis- tance problem between the reduced convex hulls of the two classes [8], or formally dist (convµ ({xi | yi = +1}) , convµ ({xi | yi = −1})) , where convµ(P ) := (X p∈P αpp ˛̨̨̨ ˛ 0 ≤ αp ≤ µ, X p∈P αp = 1 ) is the reduced convex hull of a set of points, for a given parameter µ, 0 ≤ µ ≤ 1.”
A second-order method for strongly convex ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}-re (2013, background): “Continuation schemes are generally well-known among optimizers [1,10,14,15,25,43,44,46], they can speed-up a good solver, unfortunately, they are difficult to analyze.”
Sparse Reconstruction by Separable Approximation (2008, unknown): “These include active-set-based homotopy algorithms [33], [56], [63], and interior-point methods [9], [10], [15], [53], [67].”
Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems (2007, methodology): “The method in [39] provides the solution path for (1), for a range of values of τ .”
Fixed-Point Continuation for l1-Minimization: Methodology and Convergence (2008, background): “Thus LARS and other homotopy algorithms [43, 49, 63] solve (6.”