From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images

By Alfred Marcel Bruckstein, David L. Donoho, Michael Elad. 2009

2,385 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition, Speech & Audio

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Citations in the corpus

Analysis of a Random Forests Model (2010, background): “Such signals have few non-zero coeﬃcients and can therefore be described as sparse in the signal domain (see for instance [14]).”
Compressed Sensing (2012, background): “We would also like to draw the reader’s attention to the recent books [29] and [32] as well as the survey article [7].”
Proximal Algorithms (2013, background): “[201], sum-of-norms regularization [156], the CAP family of penalties [206], l1 trend filtering [114], covariance selection [71], sparse recovery [43], basis pursuit [56], Huber loss [105], singular value thresholding [45], and sparse graph selection [138].”
Classification and clustering via dictionary learning with structured incoherence and shared features (2010, background): “due in part to the fact that an important variety of signals such as audio and natural images can be well approximated by a linear combination of a few elements (atoms) of some (often) redundant basis, usually called dictionaries [2].”
Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality (2008, background): “So the following problem comes under consideration (see [21, 19, 27]) min{‖x‖0 : Ax = b} (32) where ‖x‖0 is the so-called l “norm” which counts the nonzero components of x ∈ R, A is an m × n matrix (m < n) and b ∈ R; the set of contraints C = {x ∈ R : Ax = b} is supposed nonvoid.”
High-resolution hyperspectral imaging via matrix factorization (2011, methodology): “The proposed method can efficiently obtain very accurate spectrum estimates with a significant resolution gap between the high-resolution RGB camera and low-resolution hyperspectral camera.”
Compressed Channel Sensing: A New Approach to Estimating Sparse Multipath Channels (2010, background): “Compressed sensing (CS) is a relatively new area of theoretical research that lies at the intersection of a number o f other research areas such as signal processing, statistics , and computational harmonic analysis; see [57]–[59] for a tutor ial overview of some of the foundational developments in ”
Sparse Dictionary Learning for Edit Propagation of High-Resolution Images (2014, methodology): “Our approach follows the principles of sparse representations [2] and signal decorrelation using the Kullback-Leibler or KL divergence (i.”
A Statistical Prediction Model Based on Sparse Representations for Single Image Super-Resolution (2014, methodology): “Finally, we briefly mention the sparsity-based synthesis model (for a comprehensive review see [25]).”
On the Role of Sparse and Redundant Representations in Image Processing (2010, methodology): “The denoising problem posed in (6) can be solved (at least approximately) by greedy techniques, if the dimensions involved are relatively low (n ≤ 1000) [7].”
Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images (2011, neutral): “, images) [1], [4], [12], [13], [24]–[26], [27], [28], [30], [31], [41].”
Seismic inversion based on L1-norm misfit function and total variation regularization (2014, methodology): “From the definition of reflection coefficient we can see that the first order TVR for m is equivalent to the sparse regularization (Bruckstein et al., 2009; Candes and Tao, 2006; Candes et al., 2006a, 2006b; Claerbout and Muir, 1973) for r, and the second order TVR for m is equivalent to the first…”
Nonlocally Centralized Sparse Representation for Image Restoration (2013, background): “In order for an effective regularizer, it is of great importance to find and model the appropriate prior knowledge of natural images, and various image prior models have been developed [5]–[8], [14], [17], [18], [22].”
Fast ℓ1-minimization algorithms and an application in robust face recognition: A review (2010, background): “benchmark the performance of the five fast `1-min algorithms on random sparse signals, namely, TNIPM/L1LS, Homotopy, SpaRSA, FISTA, and YALL1, together with the classical OMP algorithm [14], [41], [17], [8] as the baseline.”
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations (2011, neutral): “[4, 11, 56].”