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

139 Scopus citations

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

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

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