Sampling and reconstructing diffusion fields in presence of aliasing

Ranieri, Juri; Vetterli, Martin

doi:10.1109/icassp.2013.6638710

Cited by 11 publications

(12 citation statements)

References 18 publications

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“…This can be because the essential bandwidth of spatial fields change with time [25], or because the field being observed is not characterized for bandwidth, or because the sampling path is not a straight line. 5 Under some technical assumptions, an algorithm is outlined to find the bandwidth b of the field in an asymptotic setting where the sampling rate n increases asymptotically.…”

Section: Bandwidth Determination Using Field Samples Obtained On mentioning

confidence: 99%

On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Mobile Sensor

Kumar

2017

IEEE Trans. Inform. Theory

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Abstract-Sampling of physical fields with mobile sensor is an emerging area. In this context, this work introduces and proposes solutions to a fundamental question: can a spatial field be estimated from samples taken at unknown sampling locations?Unknown sampling location, sample quantization, unknown bandwidth of the field, and presence of measurement-noise present difficulties in the process of field estimation. In this work, except for quantization, the other three issues will be tackled together in a mobile-sampling framework. Spatially bandlimited fields are considered. It is assumed that measurement-noise affected field samples are collected on spatial locations obtained from an unknown renewal process. That is, the samples are obtained on locations obtained from a renewal process, but the sampling locations and the renewal process distribution are unknown. In this unknown sampling location setup, it is shown that the mean-squared error in field estimation decreases as O(1/n) where n is the average number of samples collected by the mobile sensor. The average number of samples collected is determined by the inter-sample spacing distribution in the renewal process. An algorithm to ascertain spatial field's bandwidth is detailed, which works with high probability as the average number of samples n increases. This algorithm works in the same setup, i.e., in the presence of measurement-noise and unknown sampling locations.

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Section: Bandwidth Determination Using Field Samples Obtained On mentioning

confidence: 99%

On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Mobile Sensor

Kumar

2017

IEEE Trans. Inform. Theory

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“…Our work also has similarities with [21,23,26,27]. These works studied the spatiotemporal sampling and reconstruction problem in the continuous diffusion field f (x, t) = A t f (x), where f (x) = f (x, 0) is the initial signal and A t is the time varying Gaussian convolution kernel determined by the diffusion rule.…”

Section: Problem 12mentioning

confidence: 99%

“…We assign a finite nonnegative integer l i to each i ∈ Ω. Under what conditions on Ω and l i is the sequence Problem 1.2 is motivated by the spatiotemporal sampling and reconstruction problem arising in spatially invariant evolution systems [1,2,3,6,7,8,21,23,26,27]. Let f ∈ ℓ 2 (I) be an unknown vector that is evolving under the iterated actions of a convolution operator A, such that at time instance t = n it evolves to be A n f .…”

Section: Problem 12mentioning

confidence: 99%

“…We list the results in [10] here. To understand their results, we need the definition in [10] In the spatiotemporal sampling problem of the heat diffusion process, a common approach is to place the sensors indexed by Ω in a periodic nonuniform way ( [21,23,26,27] and reference therein). Let m be a positive divisor of d such that d = mJ, and we also investigate when a union of periodic sets Ω = {mZ d + r, r ∈ W ⊂ Z m } is an admissible set for an operator A defined by a convolution kernel a ∈ ℓ 2 (Z d ).…”

Section: Single Variable Casementioning

confidence: 99%

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Universal Spatiotemporal Sampling Sets for Discrete Spatially Invariant Evolutionary Systems

Tang

2017

IEEE Trans. Inform. Theory

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Abstract. Let (I, +) be a finite abelian group and A be a circular convolution operator on ℓ 2 (I). The problem under consideration is how to construct minimal Ω ⊂ I and li such that Y = {ei, Aei, · · · , A l i ei : i ∈ Ω} is a frame for ℓ 2 (I), where {ei : i ∈ I} is the canonical basis of ℓ 2 (I). This problem is motivated by the spatiotemporal sampling problem in discrete spatially invariant evolution systems. We will show that the cardinality of Ω should be at least equal to the largest geometric multiplicity of eigenvalues of A, and we consider the universal spatiotemporal sampling sets (Ω, li) for convolution operators A with eigenvalues subject to the same largest geometric multiplicity. We will give an algebraic characterization for such sampling sets and show how this problem is linked with sparse signal processing theory and polynomial interpolation theory. IntroductionLet (I, +) be a finite abelian group, we denote by ℓ 2 (I) the space of square summable complex-valued functions defined on I with the inner product given byWe denote by {e i : i ∈ I} the canonical basis of ℓ 2 (I), where e i is the characteristic function of {i} ⊂ I.Definition 1.1. The operator A on ℓ 2 (I) is called a circular convolution operator if there exists a complex-valued function a defined on I such thatThe function a is said to be the convolution kernel of A.2010 Mathematics Subject Classification. Primary 94A20, 94A12, 42C15, 15A29.

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“…Ranieri et al proposed a compressed sensing approach [10], whilst Auffray et al proposed a method based on the reciprocity gap [11]. Ranieri and Vetterli [12] have also considered uniform spatial sampling and reconstruction using classical interpolation techniques. While Rostami et al [13] introduced diffusive compressive sensing (DCS) to solve the problem.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal sampling and reconstruction of diffusion fields induced by point sources

Murray-Bruce

Dragotti

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this paper we consider a diffusion field induced by multiple point sources and address the problem of reconstructing the field from its spatio-temporal samples obtained using a sensor network. We begin by formulating the problem as a multi-source estimation problem -so estimating source locations, activation times and intensities given samples of the induced field. Next a two-step algorithm is proposed for the single (localized and instantaneous) source field. First, the source location and intensity are estimated by applying the "reciprocity gap" principle; we show that this step can also reveal locations of multiple non-instantaneous sources. In the second step, we use an iterative method, based on CauchySchwarz inequality, to find the activation time given the estimated location and intensity. Finally we extend this algorithm to the multi-source field and present simulation results to validate our findings.

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Sampling and reconstructing diffusion fields in presence of aliasing

Cited by 11 publications

References 18 publications

On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Mobile Sensor

On Bandlimited Field Estimation from Samples Recorded by a Location-Unaware Mobile Sensor

Universal Spatiotemporal Sampling Sets for Discrete Spatially Invariant Evolutionary Systems

Spatio-temporal sampling and reconstruction of diffusion fields induced by point sources

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