Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain

Paul Sajda, Shuyan Du, Truman R. Brown, Radka Stoyanova, Dikoma C. Shungu, Xiangling Mao, Lucas C. Parra

Research output: Contribution to journalArticle

132 Citations (Scopus)

Abstract

We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.

Original languageEnglish
Pages (from-to)1453-1465
Number of pages13
JournalIEEE Transactions on Medical Imaging
Volume23
Issue number12
DOIs
StatePublished - Dec 1 2004
Externally publishedYes

Fingerprint

Magnetic resonance
Factorization
Brain
Magnetic Resonance Spectroscopy
Magnetic Resonance Imaging
Recovery
Decomposition
Blind source separation
Bayes Theorem
Computational efficiency
Noise
Observation
Tissue
Processing

Keywords

  • Blind source separation (BSS)
  • Chemical shift imaging (CSI)
  • Hierarchical decomposition
  • Magnetic resonance (MR)
  • Magnetic resonance spectroscopy (MRS)
  • Nonnegative matrix factorization (NMF)

ASJC Scopus subject areas

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain. / Sajda, Paul; Du, Shuyan; Brown, Truman R.; Stoyanova, Radka; Shungu, Dikoma C.; Mao, Xiangling; Parra, Lucas C.

In: IEEE Transactions on Medical Imaging, Vol. 23, No. 12, 01.12.2004, p. 1453-1465.

Research output: Contribution to journalArticle

Sajda, Paul ; Du, Shuyan ; Brown, Truman R. ; Stoyanova, Radka ; Shungu, Dikoma C. ; Mao, Xiangling ; Parra, Lucas C. / Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain. In: IEEE Transactions on Medical Imaging. 2004 ; Vol. 23, No. 12. pp. 1453-1465.
@article{773b5f2b94704e179fec3ac9d59f5887,
title = "Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain",
abstract = "We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.",
keywords = "Blind source separation (BSS), Chemical shift imaging (CSI), Hierarchical decomposition, Magnetic resonance (MR), Magnetic resonance spectroscopy (MRS), Nonnegative matrix factorization (NMF)",
author = "Paul Sajda and Shuyan Du and Brown, {Truman R.} and Radka Stoyanova and Shungu, {Dikoma C.} and Xiangling Mao and Parra, {Lucas C.}",
year = "2004",
month = "12",
day = "1",
doi = "10.1109/TMI.2004.834626",
language = "English",
volume = "23",
pages = "1453--1465",
journal = "IEEE Transactions on Medical Imaging",
issn = "0278-0062",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "12",

}

TY - JOUR

T1 - Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain

AU - Sajda, Paul

AU - Du, Shuyan

AU - Brown, Truman R.

AU - Stoyanova, Radka

AU - Shungu, Dikoma C.

AU - Mao, Xiangling

AU - Parra, Lucas C.

PY - 2004/12/1

Y1 - 2004/12/1

N2 - We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.

AB - We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.

KW - Blind source separation (BSS)

KW - Chemical shift imaging (CSI)

KW - Hierarchical decomposition

KW - Magnetic resonance (MR)

KW - Magnetic resonance spectroscopy (MRS)

KW - Nonnegative matrix factorization (NMF)

UR - http://www.scopus.com/inward/record.url?scp=10044269618&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10044269618&partnerID=8YFLogxK

U2 - 10.1109/TMI.2004.834626

DO - 10.1109/TMI.2004.834626

M3 - Article

C2 - 15575404

AN - SCOPUS:10044269618

VL - 23

SP - 1453

EP - 1465

JO - IEEE Transactions on Medical Imaging

JF - IEEE Transactions on Medical Imaging

SN - 0278-0062

IS - 12

ER -