Just relax: convex programming methods for identifying sparse signals in noise

By Joel A. Tropp. 2006

1,498 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Signal Processing

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Citations in the corpus

Learning generative models for protein fold families (2011, background): “See [21] for a recent review of L 1 -regularization.”
Nearly unbiased variable selection under minimax concave penalty (2010, background): “14) p* > o^w?{2/n) \og{d?/e) + 9fX and X > X\^/(l ? #|)+, where 0f = sgn(j8AO)||oo and 0| = ||?(A^,A"?A<! sgn(/}AO)||oo [Mein shausen and Buhlmann (2006), Tropp (2006), Zhao and Yu (2006) and Wain wright (2006)].”
High-dimensional Ising model selection using ℓ1-regularized logistic regression (2010, background): “The Annals of Statistics 2010, Vol. 38, No. 3, 1287–1319 DOI: 10.1214/09-AOS691 © Institute of Mathematical Statistics, 2010 HIGH-DIMENSIONAL ISING MODEL SELECTION USING 1-REGULARIZED LOGISTIC REGRESSION”
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification (2009, methodology): “The renewed interest in nuclear norm minimization is motivated by the remarkable success of l1-norm techniques in practice, and by theoretical results that characterize the possibility of exact recovery of sparse signals by l1-norm methods [17, 10, 9, 8, 44 ].”
Compressed Sensing for Real-Time Energy-Efficient ECG Compression on Wireless Body Sensor Nodes (2011, methodology): “The latter is encoded using lossless Huffman coding to produce the encoded vector c.”
Multitask Sparsity via Maximum Entropy Discrimination (2011, methodology): “While a survey of sparsity is out of the scope of this article, one of the most popular implementations of sparsity or selection in regression settings is theℓ1 regularized Lasso method and its variants (Tibshirani, 1996; Tropp, 2006).”
An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive sensing (2010, background): “The related studies [21, 22, 23, 27, 28] have also inspired the nourishing research in the compressive sensing area.”
Sharp thresholds for high-dimensional and noisy recovery of sparsity (2006, background): “, 4], [12], [13], [14], [15], [2], [16].”
Convolutional Neural Networks Analyzed via Convolutional Sparse Coding (2016, methodology): “The above has a convex relaxation in the form of the Basis-Pursuit (BP) problem (Chen et al., 2001; Donoho and Elad, 2003; Tropp, 2006), formally defined as (P1) : min Γ ‖Γ‖1 s.t. DΓ = X. (4) Many questions arise from the above two defined problems.”
Comparing Measures of Sparsity (2008, background): “…has also played a central role in the success of many machine learning algorithms and techniques such as matrix factorization [7], signal recovery/extraction [8], denoising [9], [10], compressed sensing [11], dictionary learning [12], signal representation [13], [14], support vector machines…”
Learning Multiscale Sparse Representations for Image and Video Restoration (2008, methodology): “Section 3 is devoted to the presentation of our multiscale scheme, and this section is followed by two sections that introduce important algorithmic improvements to the original single-scale K-SVD.”
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit (2017, background): “information criteria such as AIC or BIC [44]”