Shift- and stretch-invariant non-negative matrix factorization with an application to brain tissue delineation in emission tomography data
2026-04-09 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a new method to analyze brain imaging data that changes over time, like those tracking how substances move in the brain. This data can be tricky because it gets stretched or shifted in time, which confuses regular analysis methods. Their approach can adjust for these shifts and stretching to better understand the brain's structure. They tested their method on simulated and real brain data, showing it works well for these complex time effects.
dynamic neuroimagingemission tomographyradiotracer transportnon-negative matrix factorizationtemporal shiftstemporal stretchingfrequency domainPyTorchphase modificationbrain tissue characterization
Authors
Anders S. Olsen, Miriam L. Navarro, Claus Svarer, Jesper L. Hinrich, Morten Mørup, Gitte M. Knudsen
Abstract
Dynamic neuroimaging data, such as emission tomography measurements of radiotracer transport in blood or cerebrospinal fluid, often exhibit diffusion-like properties. These introduce distance-dependent temporal delays, scale-differences, and stretching effects that limit the effectiveness of conventional linear modeling and decomposition methods. To address this, we present the shift- and stretch-invariant non-negative matrix factorization framework. Our approach estimates both integer and non-integer temporal shifts as well as temporal stretching, all implemented in the frequency domain, where shifts correspond to phase modifications, and where stretching is handled via zero-padding or truncation. The model is implemented in PyTorch (https://github.com/anders-s-olsen/shiftstretchNMF). We demonstrate on synthetic data and brain emission tomography data that the model is able to account for stretching to provide more detailed characterization of brain tissue structure.