Recovery of exact sparse representations in the presence of bounded noise

By Jean-Jacques Fuchs. 2005

331 citations recorded by the source corpus.

Subfields: Applied Mathematics, Biomedical Engineering, Computational Mechanics

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Citations in the corpus

Lifelong Policy Gradient Learning of Factored Policies for Faster Training Without Forgetting (2020, background): “Following the argument of Fuchs [13], we reach the following conditions: Let γ be the set of indices j such that (cid:12)(cid:12)(cid:12) ρ L , H ( t ) , g ( t ) , α ( t ) , j (cid:17)(cid:12)(cid:12)(cid:12) = µ .”
Data-driven inversion-based control of nonlinear systems (2015, background): “In step 4, the (cid:96) 1 norm of the coeﬃcient vector β is minimized, leading to a sparse coeﬃcient vector α , i.e. a vector with a “small” number of non-zero elements, Fuchs (2005); Donoho et al. (2006); Candes et al. (2006); Tropp (2006).”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, background): “The work reported in [48, 80, 157] offers such results, but requires more strict (and thus less realistic) conditions.”
LASSO-TYPE RECOVERY OF SPARSE REPRESENTATIONS FOR HIGH-DIMENSIONAL DATA (2008, background): “For the equivalence between !1- and !0-sparse solutions see, for example, Donoho [8], Donoho and Elad [9], Fuchs [12], Gribonval and Nielsen [14], Tropp [30, 31].”
The Lasso Problem and Uniqueness (2012, background): “For example, see Osborne et al. (2000 b ), Fuchs (2005), Wainwright (2009), Candes & Plan (2009).”
Online dictionary learning for sparse coding (2009, background): “This matrix is thus invertible and classical results (Fuchs, 2005) ensure the uniqueness of the sparse coding solution.”
Task-Driven Dictionary Learning (2010, background): “Proof: Equation (20) can be obtained by considering subgradient optimality conditions as done in [57] for the case λ2 = 0.”
A SIGNIFICANCE TEST FOR THE LASSO (2013, background): “…& Teboulle (2009), Friedman et al. (2010), Becker, Bobin & Candes (2011), Boyd et al. (2011), Becker, Candes & Grant (2011); and for theoretical work see, e.g., Greenshtein & Ritov (2004), Fuchs (2005), Donoho (2006), Candes & Tao (2006), Zhao & Yu (2006), Wainwright (2009), Candes & Plan (2009).”
Just relax: convex programming methods for identifying sparse signals in noise (2006, background): “After the first draft [25] of this paper had been completed, it came to the author’s attention that several other researchers were preparing papers on the performance of convex relaxation in the presence of noise [18, 26, 27].”
Strong rules for discarding predictors in lasso-type problems (2010, background): “…condition appearing in work about model selection properties of the lasso is the ‘irrepresentable condition’ (Zhao and Yu, 2006; Wainwright, 2009; Candes and Plan, 2009), which is closely related to the concept of ‘mutual incoherence’ (Fuchs, 2005; Tropp, 2006; Meinshausen and Buhlmann, 2006).”
Necessary and sufficient conditions for linear convergence of ℓ1‐regularization (2011, unknown): “2) with `1-regularization term (see [11, 16, 22, 36]), i.”