Modified-CS: Modifying compressive sensing for problems with partially known support

By Namrata Vaswani, Wei Lu. 2009 IEEE International Symposium on Information Theory, 2009

561 citations recorded by the source corpus.

We study the problem of reconstructing a sparse signal from a limited number of its linear projections when a part of its support is known. This may be available from prior knowledge. Alternatively, in a problem of recursively reconstructing time sequences of sparse spatial signals, one may use the support estimate from the previous time instant as the “known” part of the support. The idea of our solution (modified-CS) is to solve a convex relaxation of the following problem: find the signal that satisfies the data constraint and whose support contains the smallest number of new additions to the known support. We obtain sufficient conditions for exact reconstruction using modified-CS. These turn out to be much weaker than those needed for CS, particularly when the known part of the support is large compared to the unknown part.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/124b3dbe1ead95fca80b8a86b5d9b22de041c1a9

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Citations in the corpus

Tradeoffs Between Convergence Speed and Reconstruction Accuracy in Inverse Problems (2016, methodology): “Section IV addresse s the relationship between our results and sparse recovery w ith side information [15], [22], [28], [29].”
Dynamical Models and tracking regret in online convex programming (2013, background): “…interest in using models of temporal structure to improve time series estimation from compressed sensing observations (Angelosante et al., 2009; Vaswani & Lu, 2010) or for time-varying networks (Snijders, 2001; Kolar et al., 2010); the associated algorithms, however, are typically batch…”
Online Optimization in Dynamic Environments (2013, background): “There has been significant recent interest in using models of temporal structure to improve time series estimation from compressed sensing observations [51, 52]; the associated algorithms, however, are typically batch methods poorly suited to large quantities of streaming data.”
Online Convex Optimization in Dynamic Environments (2015, background): “There has been signiﬁcant recent interest in using models of temporal structure to improve time series estimation from compressed sensing observations [52], [53]; the associated algorithms, however, are typically batch methods poorly suited to large quantities of streaming data.”
Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery (2017, methodology): “Thus, instead of recovering the outlier vector and its support via l 1 minimization (or CoSaMP etc), it uses the modiﬁed-CS idea [45].”
RODEO: Robust DE-aliasing autoencOder for real-time medical image reconstruction (2017, methodology): “In [30], the reference frame was taken as the previous frame; in [31] the reference frame was predicted using an auto-regressive filter.”
Signal Processing With Compressive Measurements (2010, methodology): “Thus, our approach provides an alternative method for solving and analyzing the problem of CS recovery with partially known support considered in [48].”