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Sampleoptimal averagecase sparse Fourier transform in two dimensions
, 2013
"... We present the first sampleoptimal sublinear time algorithms for the sparse Discrete Fourier Transform over a twodimensional √ n × √ n grid. Our algorithms are analyzed for average case signals. For signals whose spectrum is exactly sparse, our algorithms use O(k) samples and run in O(k log k) ti ..."
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Cited by 13 (7 self)
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We present the first sampleoptimal sublinear time algorithms for the sparse Discrete Fourier Transform over a twodimensional √ n × √ n grid. Our algorithms are analyzed for average case signals. For signals whose spectrum is exactly sparse, our algorithms use O(k) samples and run in O(k log k) time, where k is the expected sparsity of the signal. For signals whose spectrum is approximately sparse, our algorithm uses O(k log n) samples and runs in O(k log 2 n) time; the latter algorithm works for k = Θ ( √ n). The number of samples used by our algorithms matches the known lower bounds for the respective signal models. By a known reduction, our algorithms give similar results for the onedimensional sparse Discrete Fourier Transform when n is a power of a small composite number (e.g.,n = 6 t).
Compressive multiplexers for correlated signals
 in Proc. IEEE Asilomar Conf. on Sig. Sys. and Comp
, 2012
"... We present a general architecture for the acquisition of ensembles of correlated signals. The signals are multiplexed onto a single line by mixing each one against a different code and then adding them together, and the resulting signal is sampled at a high rate. We show that if the M signals, each ..."
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Cited by 3 (1 self)
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We present a general architecture for the acquisition of ensembles of correlated signals. The signals are multiplexed onto a single line by mixing each one against a different code and then adding them together, and the resulting signal is sampled at a high rate. We show that if the M signals, each bandlimited to W/2 Hz, can be approximated by a superposition of R < M underlying signals, then the ensemble can be recovered by sampling at a rate within a logarithmic factor of RW (as compared to the Nyquist rate of MW). This sampling theorem shows that the correlation structure of the signal ensemble can be exploited in the acquisition process even though it is unknown a priori. The reconstruction of the ensemble is recast as a lowrank matrix recovery problem from linear measurements. The architectures we are considering impose a certain type of structure on the linear operators. Although our results depend on the mixing forms being random, this imposed structure results in a very different type of random projection than those analyzed in the lowrank recovery literature to date. 1
GHzWide Sensing and Decoding Using the Sparse Fourier Transform
"... GHz of spectrum in realtime without sampling the signal at GS/s –i.e., without high speed ADCs. Further, it is simple and can be implemented on commodity lowpower radios. Our approach builds on recent advances in the area of sparse Fourier transforms, which show that it is possible to reconstruct a ..."
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Cited by 3 (1 self)
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GHz of spectrum in realtime without sampling the signal at GS/s –i.e., without high speed ADCs. Further, it is simple and can be implemented on commodity lowpower radios. Our approach builds on recent advances in the area of sparse Fourier transforms, which show that it is possible to reconstruct a sparse signal without sampling it at the Nyquist rate. To demonstrate our design, we implement it using 3 software radios, each sampling the spectrum at 50 MS/s, producing a device that captures 0.9 GHz — i.e., 6 × larger digital bandwidth than the three software radios combined. Finally, an extension of BigBand can perform GHz spectrum sensing even in scenarios where the spectrum is not sparse. 1
Design of Energyefficient Sensing Systems with Direct Computations on Compressivelysensed Data
, 2013
"... The aim of this thesis is to explore the energy limits that can be achieved by signalprocessing systems when they explicitly utilize signal representations that encode information efficiently. Compressive sensing is one method that enables us to efficiently represent data. The challenge, however, ..."
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The aim of this thesis is to explore the energy limits that can be achieved by signalprocessing systems when they explicitly utilize signal representations that encode information efficiently. Compressive sensing is one method that enables us to efficiently represent data. The challenge, however, is that in compressive sensing, signals get substantially altered due to the random projections involved, posing a challenge for signal analysis. Moreover, due to the high energy costs, reconstructing signals before analysis is also often infeasible. In this thesis, we develop methodologies that enable us to directly perform analysis on embedded signals that are compressively sensed. Thus, our approach helps potentially reduce the energy and/or resources required for computation, communication, and storage in sensor networks. We specifically focus on transforming linear signalprocessing computations so that they can be applied directly to compressivelysensed signals. We show that this can be achieved by solving a system of linear equations, where we solve for a projection of the processed signals as opposed to the processed signals themselves. This opens up two ap
Edinburgh Research Explorer
"... An efficient implementation of the lowcomplexity multicoset subNyquist wideband radar electronic surveillance Citation for published version: ..."
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An efficient implementation of the lowcomplexity multicoset subNyquist wideband radar electronic surveillance Citation for published version:
Finding Zeros: Greedy Detection of Holes
"... Abstract—In this paper, motivated by the setting of whitespace detection [1], we present theoretical and empirical results for detection of the zerosupport E of x ∈ Cp (xi = 0 for i ∈ E) with reduceddimension linear measurements. We propose two lowcomplexity algorithms based on onestep threshol ..."
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Abstract—In this paper, motivated by the setting of whitespace detection [1], we present theoretical and empirical results for detection of the zerosupport E of x ∈ Cp (xi = 0 for i ∈ E) with reduceddimension linear measurements. We propose two lowcomplexity algorithms based on onestep thresholding [2] for this purpose. The second algorithm is a variant of the first that further assumes the presence of groupstructure in the target signal [3] x. Performance guarantees for both algorithms based on the worstcase and average coherence (group coherence) of the measurement matrix is presented along with the empirical performance of the algorithms.
1Modulated UnitNorm Tight Frames for Compressed Sensing
"... Abstract—In this paper, we propose a compressed sensing (CS) framework that consists of three parts: a unitnorm tight frame (UTF), a random diagonal matrix and a columnwise orthonormal matrix. We prove that this structure satisfies the restricted isometry property (RIP) with high probability if th ..."
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Abstract—In this paper, we propose a compressed sensing (CS) framework that consists of three parts: a unitnorm tight frame (UTF), a random diagonal matrix and a columnwise orthonormal matrix. We prove that this structure satisfies the restricted isometry property (RIP) with high probability if the number of measurements m = O(s log2 s log2 n) for ssparse signals of length n and if the columnwise orthonormal matrix is bounded. Some existing structured sensing models can be studied under this framework, which then gives tighter bounds on the required number of measurements to satisfy the RIP. More importantly, we propose several structured sensing models by appealing to this unified framework, such as a general sensing model with arbitrary/determinisic subsamplers, a fast and efficient block compressed sensing scheme, and structured sensing matrices with deterministic phase modulations, all of which can lead to improvements on practical applications. In particular, one of the constructions is applied to simplify the transceiver design of CSbased channel estimation for orthogonal frequency division multiplexing (OFDM) systems. Index Terms—Compressed sensing, structured sensing matrix, unitnorm tight frame, coherence analysis, arbitrary/deterministic subsampling, phase modulation, Golay sequence. I.