  We compare calcium ion signaling ($\mathrm {Ca}^{2+}$) 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 unbiased manner. Finally, the $\mathrm {Ca}^{2+}$ 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 $\mathrm
{Ca}^{2+}$ signals. Our signal extraction methods then lead to simple although
finely focused statistical methods to compare $\mathrm {Ca}^{2+}$ signals
across experimental conditions.
