Use of multiple singular value decompositions to analyze complex intracellular calcium ion signals

Josue G. Martinez, Jianhua Z. Huang, Robert C. Burghardt, Rola Barhoumi, Raymond J. Carroll

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We compare calcium ion signaling (Ca(2+)) between two exposures; the data are present as movies, or, more prosaically, time series of images. This paper describes novel uses of singular value decompositions (SVD) and weighted versions of them (WSVD) to extract the signals from such movies, in a way that is semi-automatic and tuned closely to the actual data and their many complexities. These complexities include the following. First, the images themselves are of no interest: all interest focuses on the behavior of individual cells across time, and thus, the cells need to be segmented in an automated manner. Second, the cells themselves have 100+ pixels, so that they form 100+ curves measured over time, so that data compression is required to extract the features of these curves. Third, some of the pixels in some of the cells are subject to image saturation due to bit depth limits, and this saturation needs to be accounted for if one is to normalize the images in a reasonably un-biased manner. Finally, the Ca(2+) signals have oscillations or waves that vary with time and these signals need to be extracted. Thus, our aim is to show how to use multiple weighted and standard singular value decompositions to detect, extract and clarify the Ca(2+) signals. Our signal extraction methods then lead to simple although finely focused statistical methods to compare Ca(2+) signals across experimental conditions.
Original languageEnglish (US)
Pages (from-to)1467-1492
Number of pages26
JournalThe Annals of Applied Statistics
Issue number4
StatePublished - Dec 2009
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: Supported by a postdoctoral training grant from the National Cancer Institute (CA90301).Supported by a grant from the National Cancer Institute (CA57030) and by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).Supported by a grant from the National Science Foundation (DMS-06-06580).Calcium imaging performed in the College of Veterinary Medicine & Biomedical Sciences Image Analysis Laboratory, was supported by NIH-NIEHS Grants P30-ES09106, P42-ES04917 and T32 ES07273.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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