A Theory for Sampling Signals From a Union of Subspaces

By Yue M. Lu, Minh N. Do. IEEE Transactions on Signal Processing, 2008

309 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/2af9760ed754e1af7056b35639d887076f548559

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In Applied Mathematics

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Learning with structured sparsity (2009, methodology): “While it is possible to work with blocks with non-uniform coding schemes, for simplicity examples provided in this paper only consider blocks with uniform coding, which is similar to the representation used in the Union-of-Subspaces model of Lu and Do (2008).”
Convex Optimization in Signal Processing and Communications (2009, background): “These results can also be applied more generally to signals that lie in a union of subspaces [28, 29], which are not necessarily shift invariant.”
Blind Multiband Signal Reconstruction: Compressed Sensing for Analog Signals (2007, methodology): “In [20], the authors consider minimal sampling requirement s for a union of shift-invariant subspaces, with a particular structure of sampling functions.”
Innovation Rate Sampling of Pulse Streams With Application to Ultrasound Imaging (2010, background): “Mathematically, such FRI signals conform with a broader mod el of signals lying in a union of subspaces [4]–[9].”
Sampling Theorems for Signals From the Union of Finite-Dimensional Linear Subspaces (2009, methodology): “It includes, for example • The ‘traditional’, noiseless k -sparse model as considered by Candes et al. in for example [6] and by Donoho in [9], in which x is assumed to have no more than k non-zero elements.”
Robust Recovery of Signals From a Structured Union of Subspaces (2008, background): “This setting is a special case of the more general union model treated in [24], [25].”
The Cosparse Analysis Model and Algorithms (2011, unknown): “In particular [29] shows that M is invertible on the union of subspaces ∪ γ ∈ Γ S γ if and only if M is invertible on all subspaces S γ + S θ for all γ, θ ∈ Γ.”
Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images (2011, background): “Specifically, because natural images manifest segments and self-similarity, one may view the dictionary-learning framework within a union-of-subspaces setting [15], [23].”
Structured Compressed Sensing: From Theory to Applications (2011, background): “we denote by Ui. Since the location set is unknown, there are N K possible subspaces Ui in which xmay reside. Mathematically, this means that sparse signals can be represented by a union of subspaces [15]: x2U= [m i=1 Ui; (38) where each subspace Ui, 1 im, is a K-dimensional subspace associated with”
Rank Awareness in Joint Sparse Recovery (2010, unknown): “Theorem 1 (Chen and Huo [11]).”