Sampling and Exact Reconstruction of Pulses with Variable Width

Baechler, Gilles; Scholefield, Adam; Baboulaz, Loïc; Vetterli, Martin

doi:10.1109/tsp.2017.2669900

Cited by 33 publications

(11 citation statements)

References 45 publications

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“…Another future research direction is on the extension of the approach to cases with dampened sinusoids. This may be useful for the estimation of pulses with variable width [41] in higher dimensions.…”

Section: Discussionmentioning

confidence: 99%

Efficient Multidimensional Diracs Estimation With Linear Sample Complexity

Pan

Blu

Vetterli

2018

IEEE Trans. Signal Process.

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Estimating Diracs in continuous two or higher dimensions is a fundamental problem in imaging. Previous approaches extended one-dimensional (1-D) methods, like the ones based on finite rate of innovation (FRI) sampling, in a separable manner, e.g., along the horizontal and vertical dimensions separately in 2-D. The separate estimation leads to a sample complexity of O K D for K Diracs in D dimensions, despite that the total degrees of freedom only increase linearly with respect to D. We propose a new method that enforces the continuous-domain sparsity constraints simultaneously along all dimensions, leading to a reconstruction algorithm with linear sample complexity O(K), or a gain of O K D −1 over previous FRI-based methods. The multidimensional Dirac locations are subsequently determined by the intersections of hypersurfaces (e.g., curves in 2-D), which can be computed algebraically from the common roots of polynomials. We first demonstrate the performance of the new multidimensional algorithm on simulated data: multidimensional Dirac location retrieval under noisy measurements. Then, we show results on real data: radio astronomy point source reconstruction (from LOFAR telescope measurements) and the direction of arrival estimation of acoustic signals (using Pyramic microphone arrays). Index Terms-Finite rate of innovation (FRI), continuousdomain sparsity, multidimension, point source reconstruction. 1053-587X

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Section: Discussionmentioning

confidence: 99%

Efficient Multidimensional Diracs Estimation With Linear Sample Complexity

Pan

Blu

Vetterli

2018

IEEE Trans. Signal Process.

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“…robots mapping their surroundings, time-of-flight technology may benefit from a time encoding framework which would significantly lower the sampling rate. Signals consisting of a stream of pulses appear in many other applications, including: ultrawideband communications [32], ECG acquisition and compression [33], radio-astronomy [34], image processing [35], ultrasound imaging [8] and processing of neuronal signals [36].…”

Section: Introductionmentioning

confidence: 99%

Reconstructing Classes of Non-Bandlimited Signals From Time Encoded Information

Alexandru

Dragotti

2020

IEEE Trans. Signal Process.

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We investigate time encoding as an alternative method to classical sampling, and address the problem of reconstructing classes of non-bandlimited signals from timebased samples. We consider a sampling mechanism based on first filtering the input, before obtaining the timing information using a time encoding machine. Within this framework, we show that sampling by timing is equivalent to a non-uniform sampling problem, where the reconstruction of the input depends on the characteristics of the filter and on its non-uniform shifts. The classes of filters we focus on are exponential and polynomial splines, and we show that their fundamental properties are locally preserved in the context of non-uniform sampling. Leveraging these properties, we then derive sufficient conditions and propose novel algorithms for perfect reconstruction of classes of nonbandlimited signals such as: streams of Diracs, sequences of pulses and piecewise constant signals. Next, we extend these methods to operate with arbitrary filters, and also present simulation results on synthetic noisy data.

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“…The needed samples F (A ℓ f ) are in this case of the form F (A ℓ f ) = F (S ℓ 1 f ) = F (f (· + ℓ)) = f (ℓ). There have been other attempts to generalize the idea of Prony's method to different expansions, including sparse polynomials [2], piecewise sinusoidal signals [3], sparse expansions into Legendre polynomials [14] or Chebyshev polynomials [21] and into Lorentzians [1]. All these expansions can be also recovered directly using the approach in [13].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Operator Based Prony Method

Stampfer

Plonka

2020

Constr Approx

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The generalized Prony method introduced in [13] is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansions into eigenfunctions of a linear operator A. However, this procedure requires the evaluation of higher powers of the linear operator A that are often expensive to provide.In this paper we propose two important extensions of the generalized Prony method that simplify the acquisition of the needed samples essentially and at the same time can improve the numerical stability of the method. The first extension regards the change of operators from A to ϕ(A), where ϕ is an analytic function, while A and ϕ(A) possess the same set of eigenfunctions. The goal is now to choose ϕ such that the powers of ϕ(A) are much simpler to evaluate than the powers of A. The second extension concerns the choice of the sampling functionals. We show, how new sets of different sampling functionals F k can be applied with the goal to reduce the needed number of powers of the operator A (resp. ϕ(A)) in the sampling scheme and to simplify the acquisition process for the recovery method.

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Sampling and Exact Reconstruction of Pulses with Variable Width

Cited by 33 publications

References 45 publications

Efficient Multidimensional Diracs Estimation With Linear Sample Complexity

Efficient Multidimensional Diracs Estimation With Linear Sample Complexity

Reconstructing Classes of Non-Bandlimited Signals From Time Encoded Information

The Generalized Operator Based Prony Method

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