Signal Reconstruction From Noisy Random Projections

By Jarvis D. Haupt, Robert D. Nowak. IEEE Transactions on Information Theory, 2006

670 citations recorded by the source corpus.

Subfields: Applied Mathematics, Biomedical Engineering, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/1511f61d5a05d85e8febdfcb6261cb9380b73ba8

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In Applied Mathematics

In Biomedical Engineering

In Computational Mechanics

Citations in the corpus

Block Compressed Sensing of Images Using Directional Transforms (2010, methodology): “As an alternative to the pursuits class of CS reconstruction, techniques based on projections have been proposed recently (e.g., [6]).”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, background): “, A ⊂ B ⇒ F (A) 6 F (B)) – Explicit prior knowledge on supports (Haupt and Nowak, 2006; Baraniuk et al., 2008; Huang et al., 2009) • Define Θ(w) = F (Supp(w)): How to get its convex envelope? 1.”
Distributed Compressive Sensing (2009, neutral): “Tothebestofourknowledge,theonlyworktodatethatappliesCSinamulti- sensorsettingisHauptandNowak[38](seeSection2.”
Information fusion for wireless sensor networks: Methods, models, and classifications (2007, background): “Compressive Wireless Sensing (CWS) [Bajwa et al. 2006] is a distributed source-channel communication architecture based on compressive sampling [Haupt and Nowak 2006], for energy ef.cient estimation of sensor data that contain structural regularity.”
Multiscale CLEAN Deconvolution of Radio Synthesis Images (2008, background): “This conclusion is supported by the explosion of interest and technical advances in “compressive sampling” (18; 19; 20; 21).”
Image Compressed Sensing Using Convolutional Neural Network (2020, methodology): “[21]).”
Sparse MRI: The application of compressed sensing for rapid MR imaging (2007, positive): “CS reconstruction is known to be stable in the presence of noise (36, 37), and can also be used to further perform non-linear edge preserving denoising (29, 38) of the image.”
Compressed Sensing for Networked Data (2008, background): “as proposed in [4], for appropriately chosen regularization constants λ1 and λ2 that each depend on the noise variance.”
Machine Unlearning for Random Forests (2020, methodology): “We can also maintain comparable predictive performance to a model with no random nodes by us-ing greedy nodes in all subsequent layers, resulting in a greedy model built on top of a random projection of the input space (Haupt & Nowak, 2006).”
DART: Data Addition and Removal Trees (2020, neutral): “We can also maintain comparable predictive performance to a model with no random nodes by using deterministic nodes in all subsequent layers, essentially resulting in a greedy model built on top of a random projection of the input space (Haupt and Nowak 2006).”
Sparse Reconstruction by Separable Approximation (2008, background): “Problem (2) is a robust version of this reconstruction process, which is resilient to errors and noisy data; this and similar criteria have been proposed and analyzed in [11], [52], [81].”
Sparse Estimation with Strongly Correlated Variables using Ordered Weighted L1 Regularization (2014, methodology): “In other words, using the OWL we pay no price (in terms of the number of measurements) for the presence of strongly correlated variables.”
Compressive wireless sensing (2006, methodology): “This result follows directly from [8], where the equivalence of {¢Tw+ i} and {i} (in distribution) and the independence of {qj} and { is proved.”
Bayesian Compressive Sensing (2008, neutral): “3While previous works [23], [24] in CS do obtain ` error bounds for function estimates, the “error bars” may be more useful from a practical standpoint as discussed in the next section.”
An Introduction To Compressive Sampling (2008, background): “(One could also consider recovery programs such as the Dantzig selector [19] or a combinatorial optimization program proposed by Haupt and Nowak [20]; both algorithms have provable results in the case where the noise is Gaussian with bounded variance .)”