Sampling signals with finite rate of innovation

By Martin Vetterli, Pina Marziliano, Thierry Blu. IEEE Transactions on Signal Processing, 2002

1,180 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/66cec179cb993db56af8ea1d3c348956304267d0

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Signal Reconstruction From Noisy Random Projections (2006, background): “Another area of work related to our results concerns the reconstruction of signals with finite degrees of freedom using a small number of non-traditional samples [8], [9].”
Analog-to-Information Conversion via Random Demodulation (2006, background): “In a typical application, only a tiny fraction of this information is actually relevant; the wideband signals in many RF applications often have a large bandwidth but a small “information rate” [1].”
Innovation Rate Sampling of Pulse Streams With Application to Ultrasound Imaging (2010, methodology): “[3], [10] is one way of recovering the frequencies and is”
An Introduction To Compressive Sampling (2008, background): “Simply take 2S consecutive time points, see “What Is Comprehensive Sampling?” and [11] and [12], for example.”
Compressive Sensing (2008, background): “An example of a practical analog compressive sensing system — a so-called “analog-to-information” converter — is given in [7]; there are interesting connections to [8].”
Sparse Sampling of Signal Innovations (2008, methodology): “Importantly, this approach can be generalized to other kernels such as the (nonperiodized) sinc, the Gaussian windows [ 7 ], and more recently any window that satisfies a Strang-Fix like condition [8].”
Millimeter-Wave Cellular Wireless Networks: Potentials and Challenges (2014, methodology): “The parametrization (4) is fundamentally nonlinear and analogous to the types of models used in finite rate of innovation models [104] and compressed sensing-based channel estimation and channel sounding [105]–[108].”
Structured Compressed Sensing: From Theory to Applications (2011, methodology): “This has also led to parallel low-rate sampling schemes that combine the principles of CS with the rich theory of sampling such as the finite rate of innovation (FRI) [6]–[8] and Xampling frameworks [9], [10].”
Matrix Completion With Noise (2009, result): “We present numerical results which complement our quantitative analysis and show that, in practice, nuclear norm minimization accurately fills in the many missing entries of large low-rank matrices from just a few noisy samples.”
Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang–Fix (2007, neutral): “Acquisition Device h(t)= (−t/T) y =<x(t), (t/T−n)> n ϕ y(t) Fig.”
Foundations of Signal Processing (2014, background): “We also thank Robert Gray for reviewing the manuscript and providing many important suggestions, in particular a better approach to covering the Dirac delta function; Thierry Blu for, among other things, providing a simple proof for a particular case of the Strang–Fix theorem; Matthew Fickus for con”
Compressive Sensing [Lecture Notes] (2007, background): “x(t) has only K degrees of freedom and thus can be measured at a much lower rate [8], [9].”
Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals (2009, background): “Reconstruction is then performed by rooting a high-order polynomial [51]–[54].”
Iterative Hard Thresholding for Compressed Sensing (2008, neutral): “The recently emerging field of compressed sensing, [8], [4], [5], [3] and [7] and the related theory of signals with a finite rate of innovations [20], 1 This research was supported by EPSRC grants D000246/2 and EP/F039697/1.”
Parameter estimation for nonincreasing exponential sums by Prony-like methods (2013, background): “In the following, we recover all parameters of a nonincreasing exponential sum (1.1), if noiseless sampled data h(k) = M∑ j=1 cj e fjk = M∑ j=1 cj z k j ∈ C (k = 0, . . . , 2N − 1) (1.2) with N ≥M are given.”