Computational Methods for Sparse Solution of Linear Inverse Problems

Proceedings of the IEEE, 2010

967 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/505526d0f1922cb1805826b134d74c3a97634427

Citations in the corpus

• Sparse representation or collaborative representation: Which helps face recognition? (2011, positive): “…coded by structural primitives [1], and in recent years sparse coding or sparse representation has been widely studied to solve the inverse problems in various image restoration applications [2] [3], partially due to the progress of l 0 -norm and l 1 -norm minimization techniques [4] [5] [6].”
• Compressive Sensing in Electromagnetics - A Review (2015, neutral): “Therefore, the noise formulation considers the form [10] e y 1⁄4 Axþ z (11)”
• Federated Learning via Over-the-Air Computation (2018, neutral): “Sparse optimization and low-rank optimization have attracted much attention in machine learning, signal processing, high-dimensional statistics, as well as wireless communication [30], [31], [32], [33], [34].”
• Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization (2010, positive): “In recent years, such a sparse coding or sparse representation strategy has been widely studied to solve inverse problems, partially due to the progress of -norm and -norm minimization techniques [60].”
• Sparse Methods for Direction-of-Arrival Estimation (2016, neutral): “ pursuit (OMP), compressive sampling matching pursuit (CoSaMP) and subspace pursuit (SP) [35–40], iterative hard thresholding (IHT) [41], maximum likelihood estimation (MLE), etc. Readers can consult [42] for a review. Here we introduce convex relaxation, ‘ q optimization and MLE in the ensuing subs”
• Structured Compressed Sensing: From Theory to Applications (2011, neutral): “There exist many efficient solvers to find BP, BPIC, and BPDN solutions; for an overview, see [51].”
• Fast L1-Minimization Algorithms For Robust Face Recognition (2010, neutral): “In this paper, we are not concerned about these pursuit-type greedy algorithms, but instead refer the reader to [33], [4], [34] for a more detailed treatment of the greedy approach. under different illuminations lies closely to a low-dimensional subspace, called face subspace [37], [38].”
• Parallel and Flexible Sampling from Autoregressive Models via Langevin Dynamics (2021, neutral): “Bayesian inverse problems are explored extensively in theoretical settings, where the prior is given by a simple analytical distribution (Tropp & Wright, 2010; Knapik et al., 2011; Wang et al., 2017).”
• Spectral compressive sensing (2013, positive): “Further work includes integrating our frequency inhibition and line spectral estimation approaches into more powerful greedy [46], iterative [71], and `1-norm minimization [72] recovery algorithms, as well as obtaining a full performance characterization for the line spectral estimators used in the ”
• Compressive Coded Aperture Spectral Imaging: An Introduction (2014, neutral): “These can be grouped into one of five computational approaches [10].”
• Deep Learning Techniques for Inverse Problems in Imaging (2020, positive): “Examples of this framework include Tikhonov regularization [54], sparsity regularization in some basis or frame [55], [56], and total variation regularization [11], [57].”
• Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms (2012, neutral): “Despite the great interest in exploiting sparsity in various applications, most of the work to date has focused on recovering sparse data represented by a vector x ∈ R n from linear measurements of the form b = Ax .”
• A Proximal-Gradient Homotopy Method for the Sparse Least-Squares Problem (2012, neutral): “A nice survey of major practical algorithms for sparse approximation appeared in [37], and performance comparisons of various algorithms can be found in, e.”
• Sparse Representation for Target Detection in Hyperspectral Imagery (2011, positive): “The above problem can also be interpreted as minimizing the approximation error within a certain sparsity level subject to (13) where is a given upper bound on the sparsity level [32].”
• Sparse Representation Based Image Interpolation With Nonlocal Autoregressive Modeling (2013, neutral): “As the closest convex relaxation [28], the l1-norm”