Sampling Theorems for Signals From the Union of Finite-Dimensional Linear Subspaces

By Thomas Blumensath, M. Davies. IEEE Transactions on Information Theory, 2009

316 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/9b8527faf3a4c5b0abbeae2836d6324750b765d5

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In Biomedical Engineering

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Robust Recovery of Signals From a Structured Union of Subspaces (2008, unknown): “For example, if When H = R N for some N , x , y = N i =1 x ( i ) y ( i ) .”
Spectral compressive sensing (2013, methodology): “The model-based RIP requires for (5) to hold only for signals with sparse representations θ ∈MK [51, 53]; we denote this new property asMK-RIP to specify the dependence on the chosen signal model and change the model-based RIP constant from δK to δMK for clarity.”
Rank Awareness in Joint Sparse Recovery (2010, background): “LetX = [x,x, . . . ,x] be the rank 1 matrix such thatℓ1 minimization fails to recoverx.”
Model-Based Compressive Sensing (2008, methodology): “Theorem 1: [6] LetMK be the union ofmK subspaces of K-dimensions inR .”
Block-Sparse Signals: Uncertainty Relations and Efficient Recovery (2009, background): “Furthermore, recovery will be robust in the presence of noise and modeling errors (i.e., when the vector is not exactly block-sparse).”
Structured Compressed Sensing: From Theory to Applications (2011, background): “This question is addressed in the following proposition [16], [17], [20], [46].”
The Cosparse Analysis Model and Algorithms (2011, unknown): “Uniqueness guarantees for missing data problems such as (5) with general union of subspace models are covered in [29, 4].”
Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser (2020, background): “The theory relies on the sparsity property, which corresponds to a “union of subspaces” prior [41], and on the measurement axes being incoherent (essentially, weakly correlated) with the sparse basis.”
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals (2009, background): “…the implementation of the analog frontend (e.g. setting the number of channels, trading system 16 branches by a higher sampling rate, and some potential hardware simplifications), and for the digital stage (e.g. low-rate and realtime processing, handling time-varying spectrum, and quantization).”