On Bandlimited Signal Reconstruction From the Distribution of Unknown Sampling Locations

Kumar, Animesh

doi:10.1109/tsp.2015.2394248

Cited by 15 publications

(20 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…, S M will correspond to ordered Unif[0, 1] random variables. In case if nX is exponentially distributed, the mean-squared error between A gen [k] and a[k] can be shown to be O(1/n) by using existing results in the literature [14].…”

Section: Field Estimation From Samples Obtained On An Unknown Rementioning

confidence: 99%

“…Prior art: The topic of unknown but uniformly distributed sampling locations was recently introduced in the context of spatial sampling in a finite interval [14]. A detailed differentiation with this earlier work is needed, since the setup and results appear to be similar in nature.…”

mentioning

confidence: 99%

“…If n sensors are uniformly distributed in an interval, as in [14], then their ordered (noise-affected) readings can be used to obtain a bandlimited field estimate with mean-squared error of O(1/n). The derivation of this result utilizes established facts on the mean-squared deviations of ordered uniformly distributed random variables [14], [15]. It is also known that ordered uniformly distributed random variables can be understood as realizations of a Poisson renewal process [13].…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Kumar

2017

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Field Estimation From Samples Obtained On An Unknown Rementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

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

Kumar

2017

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the continuous problem that we consider in this paper, Browning proposed an alternating least squares algorithm that converges to a local minimum [16] and Kumar considered the case where the unknown sample positions are governed by a stochastic model. He was able to show that the reconstruction error is asymptotically inversely proportional to the number of samples [17] [18].…”

Section: Introductionmentioning

confidence: 99%

Sampling at Unknown Locations: Uniqueness and Reconstruction Under Constraints

Elhami

Pacholska

Haro

et al. 2018

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Traditional sampling results assume that the sample locations are known. Motivated by simultaneous localization and mapping (SLAM) and structure from motion (SfM), we investigate sampling at unknown locations. We show that, without further constraints, the problem is often hopeless. More precisely, we show that, for polynomial and bandlimited signals, it is possible to find two signals, arbitrarily far from each other, that fit the measurements. To overcome this, we propose to add constraints to the sample positions. As we show, this leads to a uniform sampling of a composite of functions. Our formulation retains the key aspects of the SLAM and SfM problems, whilst providing uniqueness, in many cases. We demonstrate this by studying two simple examples of constrained sampling at unknown locations. In the first, we consider sampling a periodic bandlimited signal composite with an unknown linear function. We derive the sampling requirements for uniqueness and present an algorithm that recovers both the bandlimited signal and the linear warping. Furthermore, we prove that, when the requirements for uniqueness are not met, the cases of multiple solutions have measure zero. For our second example, we consider polynomials sampled such that the sampling positions are constrained by a rational function. We prove that, if a specific sampling requirement is met, uniqueness is achieved. In addition, we present an alternate minimization scheme for solving the resulting nonconvex optimization problem. Finally, simulation results are provided to support our theoretical analysis.

show abstract

“…Prior art: Estimation of bandlimited fields from samples taken at unknown but statistically distributed sampling locations was studied by Kumar [10], [11]. Reconstruction of discrete-time bandlimited fields from unknown sampling locations was studied by Marziliano and Vetterli [12] in a combinatorial setting.…”

Section: Introductionmentioning

confidence: 99%

Bandlimited field reconstruction from samples obtained on a discrete grid with unknown random locations

Mallick

Kumar

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

Self Cite

View full text Add to dashboard Cite

show abstract

On Bandlimited Signal Reconstruction From the Distribution of Unknown Sampling Locations

Cited by 15 publications

References 14 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

Sampling at Unknown Locations: Uniqueness and Reconstruction Under Constraints

Bandlimited field reconstruction from samples obtained on a discrete grid with unknown random locations

Contact Info

Product

Resources

About