Journal ArticleDOI
An Introduction To Compressive Sampling
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TLDR
The theory of compressive sampling, also known as compressed sensing or CS, is surveyed, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.Abstract:
Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use.read more
Citations
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Journal ArticleDOI
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
TL;DR: This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.
Journal ArticleDOI
A collaborative framework for 3D alignment and classification of heterogeneous subvolumes in cryo-electron tomography
Oleg Kuybeda,Gabriel A. Frank,Alberto Bartesaghi,Mario J. Borgnia,Sriram Subramaniam,Guillermo Sapiro +5 more
TL;DR: The genetic identity of each virus particle present in the mixture can be assigned based solely on the structural information derived from single envelope glycoproteins displayed on the virus surface by the nuclear norm-based, collaborative alignment method presented here.
BookDOI
Statistical Learning with Sparsity: The Lasso and Generalizations
TL;DR: Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data and extract useful and reproducible patterns from big datasets.
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Inverse problems: A Bayesian perspective
TL;DR: The Bayesian approach to regularization is reviewed, developing a function space viewpoint on the subject, which allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion.
Journal ArticleDOI
A tutorial on synthetic aperture radar
Alberto Moreira,Pau Prats-Iraola,Marwan Younis,Gerhard Krieger,Irena Hajnsek,Konstantinos Papathanassiou +5 more
TL;DR: This paper provides first a tutorial about the SAR principles and theory, followed by an overview of established techniques like polarimetry, interferometry and differential interferometric as well as of emerging techniques (e.g., polarimetric SARinterferometry, tomography and holographic tomography).
References
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Journal ArticleDOI
Regression Shrinkage and Selection via the Lasso
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
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
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
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
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: It is demonstrated 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(m ln d) random linear measurements of that signal.