In Positron Emission Imaging, scans take long time (>10 mins) and obviously this is affected by patient motion, one of the main factors being respiratory motion. Patients breathe, so they "blur" the image.

A good way to fix this is to "bin" your data in different parts of the respiratory phase, i.e. reconstruct 10 images instead of 1, of the full respiratory cycle. But people breathe non-uniformly in amplitude and period, so we need to find a way to obtain a "respiratory surrogate signal", a plot that tells us for each data point where it was acquired in the respiratory phase.

Turns out that if you bin the data in e.g. 0.5 second pieces and apply Principal Component Analysis (PCA, "same thing" as SVD) to the data, and find the principal component that produces a change in value with a period of a common respiratory signal (3~6s or so) when applied to the data, you can very accurately obtain the respiratory phase.

This (or a variation of this) is nowadays clinically used in PET scanners all across the globe to correct for respiratory motion.

K. Thielemans, S. Rathore, F. Engbrant and P. Razifar, "Device-less gating for PET/CT using PCA," 2011 IEEE Nuclear Science Symposium Conference Record, 2011, pp. 3904-3910, doi: 10.1109/NSSMIC.2011.6153742.