Journal ArticleDOI
Sparsity and Compressed Sensing in Radar Imaging
Lee C. Potter,Emre Ertin,Jason T. Parker,Mujdat Cetin +3 more
- Vol. 98, Iss: 6, pp 1006-1020
TLDR
The accessible framework provided by compressed sensing illuminates the impact of joining these themes and potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.Abstract:
Remote sensing with radar is typically an ill-posed linear inverse problem: a scene is to be inferred from limited measurements of scattered electric fields. Parsimonious models provide a compressed representation of the unknown scene and offer a means for regularizing the inversion task. The emerging field of compressed sensing combines nonlinear reconstruction algorithms and pseudorandom linear measurements to provide reconstruction guarantees for sparse solutions to linear inverse problems. This paper surveys the use of sparse reconstruction algorithms and randomized measurement strategies in radar processing. Although the two themes have a long history in radar literature, the accessible framework provided by compressed sensing illuminates the impact of joining these themes. Potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.read more
Citations
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Journal ArticleDOI
On Dynamic Mode Decomposition: Theory and Applications
TL;DR: A theoretical framework in which dynamic mode decomposition is defined as the eigendecomposition of an approximating linear operator, which generalizes DMD to a larger class of datasets, including nonsequential time series, and shows that under certain conditions, DMD is equivalent to LIM.
Journal ArticleDOI
Metamaterial Apertures for Computational Imaging
John Desmond Hunt,Tom Driscoll,Tom Driscoll,Alex Mrozack,Guy Lipworth,Matthew S. Reynolds,David J. Brady,David R. Smith +7 more
TL;DR: By leveraging metamaterials and compressive imaging, a low-profile aperture capable of microwave imaging without lenses, moving parts, or phase shifters is demonstrated and allows image compression to be performed on the physical hardware layer rather than in the postprocessing stage, thus averting the detector, storage, and transmission costs associated with full diffraction-limited sampling of a scene.
Journal ArticleDOI
Compressive Sensing in Electromagnetics - A Review
TL;DR: A review of the state-of-the-art and most recent advances of compressive sensing and related methods as applied to electromagnetics can be found in this article, where a wide set of applicative scenarios comprising the diagnosis and synthesis of antenna arrays, the estimation of directions of arrival, and the solution of inverse scattering and radar imaging problems are reviewed.
Journal ArticleDOI
Robust Spectral Compressed Sensing via Structured Matrix Completion
Yuxin Chen,Yuejie Chi +1 more
TL;DR: This paper develops a novel algorithm, called enhanced matrix completion (EMaC), based on structured matrix completion that does not require prior knowledge of the model order to recover a spectrally sparse signal from a small random subset of its n time domain samples.
Journal ArticleDOI
Directions-of-Arrival Estimation Through Bayesian Compressive Sensing Strategies
TL;DR: The estimation of the directions of arrival (DoAs) of narrow-band signals impinging on a linear antenna array is addressed within the Bayesian compressive sensing (BCS) framework and customized implementations exploiting the measurements collected at a unique time instant and multiple time instants are presented and discussed.
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
Nonlinear total variation based noise removal algorithms
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.
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
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.