Sparse Sampling for Inverse Problems with Tensors

Guillermo Ortiz-Jimenez; Mario Coutino; Sundeep Prabhakar Chepuri; Geert Leus

doi:10.1109/TSP.2019.2914879

Sparse Sampling for Inverse Problems with Tensors

Guillermo Ortiz-Jimenez^*, Mario Coutino, Sundeep Prabhakar Chepuri, Geert Leus

^*Corresponding author for this work

Signal Processing Systems

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

24 Citations (Scopus)

16 Downloads (Pure)

Abstract

We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multiantenna communications to graph signal processing, to validate the developed theory.

Original language	English
Article number	8705331
Pages (from-to)	3272-3286
Number of pages	15
Journal	IEEE Transactions on Signal Processing
Volume	67
Issue number	12
DOIs	https://doi.org/10.1109/TSP.2019.2914879
Publication status	Published - 2019

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Graph signal processing
multidimensional sampling
sparse sampling
submodular optimization
tensors

Access to Document

10.1109/TSP.2019.2914879

Sparse_Sampling_for_Inverse_Problems_With_TensorsFinal published version, 1.73 MB

Cite this

@article{f2a1a715ede84f9c9a57568d16b3942d,

title = "Sparse Sampling for Inverse Problems with Tensors",

abstract = "We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multiantenna communications to graph signal processing, to validate the developed theory.",

keywords = "Graph signal processing, multidimensional sampling, sparse sampling, submodular optimization, tensors",

author = "Guillermo Ortiz-Jimenez and Mario Coutino and Chepuri, {Sundeep Prabhakar} and Geert Leus",

note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.",

year = "2019",

doi = "10.1109/TSP.2019.2914879",

language = "English",

volume = "67",

pages = "3272--3286",

journal = "IEEE Transactions on Signal Processing",

issn = "1053-587X",

publisher = "IEEE",

number = "12",

}

TY - JOUR

T1 - Sparse Sampling for Inverse Problems with Tensors

AU - Ortiz-Jimenez, Guillermo

AU - Coutino, Mario

AU - Chepuri, Sundeep Prabhakar

AU - Leus, Geert

N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

PY - 2019

Y1 - 2019

N2 - We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multiantenna communications to graph signal processing, to validate the developed theory.

AB - We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop low-complexity greedy algorithms based on submodular optimization methods to compute near-optimal sampling sets. We present several numerical examples, ranging from multiantenna communications to graph signal processing, to validate the developed theory.

KW - Graph signal processing

KW - multidimensional sampling

KW - sparse sampling

KW - submodular optimization

KW - tensors

UR - http://www.scopus.com/inward/record.url?scp=85066879521&partnerID=8YFLogxK

U2 - 10.1109/TSP.2019.2914879

DO - 10.1109/TSP.2019.2914879

M3 - Article

AN - SCOPUS:85066879521

SN - 1053-587X

VL - 67

SP - 3272

EP - 3286

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 12

M1 - 8705331

ER -

Sparse Sampling for Inverse Problems with Tensors

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this