Proceedings ArticleDOI
Theory and Implementation of an Analog-to-Information Converter using Random Demodulation
Jason N. Laska,S. Kirolos,Marco F. Duarte,T. Ragheb,Richard G. Baraniuk,Yehia Massoud +5 more
- pp 1959-1962
TLDR
The new theory of compressive sensing enables direct analog-to-information conversion of compressible signals at sub-Nyquist acquisition rates and proves the concept under the effect of circuit nonidealities.Abstract:
The new theory of compressive sensing enables direct analog-to-information conversion of compressible signals at sub-Nyquist acquisition rates. The authors develop new theory, algorithms, performance bounds, and a prototype implementation for an analog-to-information converter based on random demodulation. The architecture is particularly apropos for wideband signals that are sparse in the time-frequency plane. End-to-end simulations of a complete transistor-level implementation prove the concept under the effect of circuit nonidealities.read more
Citations
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Journal ArticleDOI
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
TL;DR: In this paper, the authors proposed simple and extremely efficient methods for solving the basis pursuit problem, which is used in compressed sensing, using Bregman iterative regularization, and they gave a very accurate solution after solving only a very small number of instances of the unconstrained problem.
Journal ArticleDOI
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals
Moshe Mishali,Yonina C. Eldar +1 more
TL;DR: This paper considers the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum, and proposes a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms.
Journal ArticleDOI
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals
TL;DR: A new type of data acquisition system, called a random demodulator, that is constructed from robust, readily available components that supports the empirical observations, and a detailed theoretical analysis of the system's performance is provided.
Proceedings ArticleDOI
Compressive Radar Imaging
TL;DR: It is demonstrated that CS has the potential to make two significant improvements to radar systems: eliminating the need for the pulse compression matched filter at the receiver, and reducing the required receiver analog-to-digital conversion bandwidth so that it need operate only at the radar reflectivity's potentially low "information rate" rather than at its potentially high Nyquist rate.
Journal ArticleDOI
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
Elaine Hale,Wotao Yin,Yin Zhang +2 more
TL;DR: The structure of optimal solution sets is studied, finite convergence for important quantities is proved, and $q$-linear convergence rates for the fixed-point algorithm applied to problems with $f(x)$ convex, but not necessarily strictly convex are established.
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
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.
Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: 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.
Journal ArticleDOI
Stable signal recovery from incomplete and inaccurate measurements
TL;DR: In this paper, the authors considered the problem of recovering a vector x ∈ R^m from incomplete and contaminated observations y = Ax ∈ e + e, where e is an error term.