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Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
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TLDR
In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.Abstract:
This report demonstrates theoretically and empirically that a greedy algorithm called
Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension
d given O(mln d) random linear measurements of that signal. This is a massive improvement
over previous results, which require O(m2) measurements. The new results for OMP are comparable
with recent results for another approach called Basis Pursuit (BP). In some settings, the
OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal
recovery problems.read more
Citations
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Compressed Sensing-Based Inpainting of Aqua Moderate Resolution Imaging Spectroradiometer Band 6 Using Adaptive Spectrum-Weighted Sparse Bayesian Dictionary Learning
TL;DR: An improved Bayesian dictionary learning algorithm based on the burgeoning compressed sensing theory can adaptively exploit the spectral relations of band 6 and other spectra to solve the problem of dead pixel stripes in MODIS.
Journal ArticleDOI
Imaging of Moving Targets With Multi-Static SAR Using an Overcomplete Dictionary
TL;DR: A method for imaging of moving targets using multi-static radar by treating the problem as one of joint spatial reflectivity signal inversion with respect to an overcomplete dictionary of target velocities to solve the moving target problem as a larger, unified regularized inversion problem subject to sparsity constraints.
Journal ArticleDOI
Review of noise removal techniques in ECG signals
Shubhojeet Chatterjee,Rini Smita Thakur,Ram Narayan Yadav,Lalita Gupta,Deepak Kumar Raghuvanshi +4 more
TL;DR: It is observed that Wavelet-VBE, EMD-MAF, GAN2, GSSSA, new MP-EKF, DLSR, and AKF are most suitable for additive white Gaussian noise removal and GAN1 is the best denoising option for composite noise removal.
Journal ArticleDOI
Self-Paced Joint Sparse Representation for the Classification of Hyperspectral Images
Jiangtao Peng,Weiwei Sun,Qian Du +2 more
TL;DR: A self-paced joint sparse representation (SPJSR) model is proposed for the classification of hyperspectral images (HSIs) and is more accurate and robust than existing JSR methods, especially in the case of heavy noise.
Journal ArticleDOI
Joint Channel Estimation and Data Rate Maximization for Intelligent Reflecting Surface Assisted Terahertz MIMO Communication Systems
TL;DR: A novel feedforward fully connected structure based deep neural network (DNN) scheme is put forward, which has the ability to learn how to output the optimal phase shift configurations by inputting the features of estimated channel.
References
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Book
Compressed sensing
TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.
Journal ArticleDOI
Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
Journal ArticleDOI
Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
Journal ArticleDOI
Least angle regression
Bradley Efron,Trevor Hastie,Iain M. Johnstone,Robert Tibshirani,Hemant Ishwaran,Keith Knight,Jean-Michel Loubes,Jean-Michel Loubes,Pascal Massart,Pascal Massart,David Madigan,David Madigan,Greg Ridgeway,Greg Ridgeway,Saharon Rosset,Saharon Rosset,Ji Zhu,Robert A. Stine,Berwin A. Turlach,Sanford Weisberg +19 more
TL;DR: A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.