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37
The pros and cons of compressive sensing for wideband signal acquisition: Noise folding vs. dynamic range
, 2011
"... Compressive sensing (CS) exploits the sparsity present in many common signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors an ..."
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Cited by 27 (5 self)
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Compressive sensing (CS) exploits the sparsity present in many common signals to reduce the number of measurements needed for digital acquisition. With this reduction would come, in theory, commensurate reductions in the size, weight, power consumption, and/or monetary cost of both signal sensors and any associated communication links. This paper examines the use of CS in the design of a wideband radio receiver in a noisy environment. We formulate the problem statement for such a receiver and establish a reasonable set of requirements that a receiver should meet to be practically useful. We then evaluate the performance of a CSbased receiver in two ways: via a theoretical analysis of the expected performance, with a particular emphasis on noise and dynamic range, and via simulations that compare the CS receiver against the performance expected from a conventional implementation. On the one hand, we show that CSbased systems that aim to reduce the number of acquired measurements are somewhat sensitive to signal noise, exhibiting a 3dB SNR loss per octave of subsampling which parallels the classic noisefolding phenomenon. On the other hand, we demonstrate that since they sample at a lower rate, CSbased systems can potentially attain a significantly larger dynamic range. Hence, we conclude that while a CSbased system has inherent limitations that do impose some restrictions on its potential applications, it also has attributes that make it highly desirable in a number of important practical settings. 1
Decentralized sparse signal recovery for compressive sleeping wireless sensor networks
 IEEE Trans. Signal Process. 2010
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SubNyquist Sampling  Bridging theory and practice
, 2011
"... Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely tuned tasks for the circuit level. Sampling theory, the gate to th ..."
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Cited by 14 (5 self)
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Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely tuned tasks for the circuit level. Sampling theory, the gate to the digital world, is the key enabling this revolution, encompassing all aspects related to the conversion of continuoustime signals to discrete streams of numbers. The famous ShannonNyquist theorem has become a landmark: a mathematical statement that has had one of the most profound impacts on industrial development of digital signal processing (DSP) systems. Over the years, theory and practice in the field of sampling have developed in parallel routes. Contributions by many research groups suggest a multitude of methods, other than uniform sampling, to acquire analog signals [1]–[6]. The math has deepened, leading to abstract signal spaces and innovative sampling techniques. Within generalized sampling theory, bandlimited signals have no special preference, other than historic. At the same time, the market adhered to the Nyquist paradigm;
Exact Support Recovery for Sparse Spikes Deconvolution
, 2013
"... This paper studies sparse spikes deconvolution over the space of measures. For nondegenerate sums of Diracs, we show that, when the signaltonoise ratio is large enough, total variation regularization (which the natural extension of ℓ 1 norm of vector to the setting of measures) recovers the exact ..."
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Cited by 11 (1 self)
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This paper studies sparse spikes deconvolution over the space of measures. For nondegenerate sums of Diracs, we show that, when the signaltonoise ratio is large enough, total variation regularization (which the natural extension of ℓ 1 norm of vector to the setting of measures) recovers the exact same number of Diracs. We also show that both the locations and the heights of these Diracs converge toward those of the input measure when the noise drops to zero. The exact speed of convergence is governed by a specific dual certificate, which can be computed by solving a linear system. Finally we draw connections between the performances of sparse recovery on a continuous domain and on a discretized grid.
Matched Filtering from Limited Frequency Samples
, 2011
"... In this paper, we study a simple correlationbased strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequencydomain samples. We model the output of this “compressive matched filter ” as a random process whose mean equals the scale ..."
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Cited by 9 (5 self)
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In this paper, we study a simple correlationbased strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequencydomain samples. We model the output of this “compressive matched filter ” as a random process whose mean equals the scaled, shifted autocorrelation function of the template signal. Using tools from the theory of empirical processes, we prove that the expected maximum deviation of this process from its mean decreases sharply as the number of measurements increases, and we also derive a probabilistic tail bound on the maximum deviation. Putting all of this together, we bound the minimum number of measurements required to guarantee that the empirical maximum of this random process occurs sufficiently close to the true peak of its mean function. We conclude that for broad classes of signals, this compressive matched filter will successfully estimate the unknown delay (with high probability, and within a prescribed tolerance) using a number of random frequencydomain samples that scales inversely with the signaltonoise ratio and only logarithmically in the in the observation bandwidth and the possible range of delays.
Compressive MUSIC: a missing link between compressive sensing and array signal processing,” Arxiv preprint arXiv:1004.4398v5
, 2010
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Spectral compressive sensing with polar interpolation
 in IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP
, 2013
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MUSIC for SingleSnapshot Spectral Estimation: Stability and Superresolution
, 2014
"... This paper studies the problem of line spectral estimation in the continuum of a bounded interval with one snapshot of array measurement. The singlesnapshot measurement data is turned into a Hankel data matrix which admits the Vandermonde decomposition and is suitable for the MUSIC algorithm. The M ..."
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Cited by 5 (0 self)
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This paper studies the problem of line spectral estimation in the continuum of a bounded interval with one snapshot of array measurement. The singlesnapshot measurement data is turned into a Hankel data matrix which admits the Vandermonde decomposition and is suitable for the MUSIC algorithm. The MUSIC algorithm amounts to finding the null space (the noise space) of the Hankel matrix, forming the noisespace correlation function and identifying the s smallest local minima of the noisespace correlation as the frequency set. In the noisefree case exact reconstruction is guaranteed for any arbitrary set of frequencies as long as the number of measurement data is at least twice the number of distinct frequencies to be recovered. In the presence of noise the stability analysis shows that the perturbation of the noisespace correlation is proportional to the spectral norm of the noise matrix as long as the latter is smaller than the smallest (nonzero) singular value of the noiseless Hankel data matrix. Under the assumption that the true frequencies are separated by at least twice the Rayleigh length, the stability of the noisespace correlation is proved by means of novel discrete Ingham inequalities which provide bounds on the largest and smallest nonzero singular values of the noiseless Hankel data matrix. The numerical performance of MUSIC is tested in comparison with other algorithms such as BLOOMP and SDP (TVmin). While BLOOMP is the stablest algorithm for frequencies separated above 4RL, MUSIC becomes the best performing one for frequencies separated between 2RL and 3RL. Also, MUSIC is more efficient than other methods. MUSIC truly shines when the frequency separation drops to one RL and below when all other methods fail. Indeed, the resolution of MUSIC apparently decreases to zero as noise decreases to zero.
Offthegrid spectral compressed sensing with prior information
 in Proc. IEEE Int. Conf. Acoust., Speech and Signal Process. (ICASSP
, 2014
"... Recent research in offthegrid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few timedomain samples even though the dictionary is continuous. In this paper, we extend offthegrid CS to applications where so ..."
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Cited by 4 (1 self)
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Recent research in offthegrid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few timedomain samples even though the dictionary is continuous. In this paper, we extend offthegrid CS to applications where some prior information about spectrally sparse signal is known. We specifically consider cases where a few contributing frequencies or poles, but not their amplitudes or phases, are known a priori. Our results show that equipping offthegrid CS with the knownpoles algorithm can increase the probability of recovering all the frequency components. Index Terms — compressed sensing, spectral estimation, basis mismatch, matrix completion, known poles 1.
PRECISE SEMIDEFINITE PROGRAMMING FORMULATION OF ATOMIC NORM MINIMIZATION FOR RECOVERING DDIMENSIONAL (D ≥ 2) OFFTHEGRID FREQUENCIES
"... Recent research in offthegrid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few timedomain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in [1] to r ..."
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Cited by 4 (2 self)
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Recent research in offthegrid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few timedomain samples even though the dictionary is continuous. In particular, atomic norm minimization was proposed in [1] to recover 1dimensional spectrally sparse signal. However, in spite of existing research efforts [2], it was still an open problem how to formulate an equivalent positive semidefinite program for atomic norm minimization in recovering signals with ddimensional (d ≥ 2) offthegrid frequencies. In this paper, we settle this problem by proposing equivalent semidefinite programming formulations of atomic norm minimization to recover signals with ddimensional (d ≥ 2) offthegrid frequencies. Index Terms — compressed sensing, spectral estimation, matrix completion, sum of squares 1.