Designing sampling schemes for multi-dimensional data

Johan Swärd; Filip Elvander; Andreas Jakobsson

doi:10.1016/j.sigpro.2018.03.011

Designing sampling schemes for multi-dimensional data

Johan Swärd^*, Filip Elvander, Andreas Jakobsson

^*Corresponding author for this work

Not published at Aalto University

Lund University

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramer-Rao lower bounds for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme. (C) 2018 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	1-10
Number of pages	10
Journal	Signal Processing
Volume	150
DOIs	https://doi.org/10.1016/j.sigpro.2018.03.011
Publication status	Published - Sept 2018
MoE publication type	A1 Journal article-refereed

Keywords

Sampling schemes
Convex optimization
Cramer-Rao lower bound
SENSOR SELECTION
CONVEX
NMR
OPTIMIZATION
RESOLUTION

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10.1016/j.sigpro.2018.03.011

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title = "Designing sampling schemes for multi-dimensional data",

abstract = "In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramer-Rao lower bounds for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme. (C) 2018 Elsevier B.V. All rights reserved.",

keywords = "Sampling schemes, Convex optimization, Cramer-Rao lower bound, SENSOR SELECTION, CONVEX, NMR, OPTIMIZATION, RESOLUTION",

author = "Johan Sw{\"a}rd and Filip Elvander and Andreas Jakobsson",

year = "2018",

month = sep,

doi = "10.1016/j.sigpro.2018.03.011",

language = "English",

volume = "150",

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journal = "Signal Processing",

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T1 - Designing sampling schemes for multi-dimensional data

AU - Swärd, Johan

AU - Elvander, Filip

AU - Jakobsson, Andreas

PY - 2018/9

Y1 - 2018/9

N2 - In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramer-Rao lower bounds for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme. (C) 2018 Elsevier B.V. All rights reserved.

AB - In this work, we propose a method for determining a non-uniform sampling scheme for multi-dimensional signals by solving a convex optimization problem reminiscent of the sensor selection problem. The resulting sampling scheme minimizes the sum of the Cramer-Rao lower bounds for the parameters of interest, given a desired number of sampling points. The proposed framework allows for selecting an arbitrary subset of the parameters detailing the model, as well as weighing the importance of the different parameters. Also presented is a scheme for incorporating any imprecise a priori knowledge of the locations of the parameters, as well as defining estimation performance bounds for the parameters of interest. Numerical examples illustrate the efficiency of the proposed scheme. (C) 2018 Elsevier B.V. All rights reserved.

KW - Sampling schemes

KW - Convex optimization

KW - Cramer-Rao lower bound

KW - SENSOR SELECTION

KW - CONVEX

KW - NMR

KW - OPTIMIZATION

KW - RESOLUTION

U2 - 10.1016/j.sigpro.2018.03.011

DO - 10.1016/j.sigpro.2018.03.011

M3 - Article

SN - 0165-1684

VL - 150

SP - 1

EP - 10

JO - Signal Processing

JF - Signal Processing

ER -

Designing sampling schemes for multi-dimensional data

Abstract

Keywords

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