Shift- and stretch-invariant non-negative matrix factorization with an application to brain tissue delineation in emission tomography data
This addresses the challenge of accurately modeling brain tissue in emission tomography for medical imaging applications, representing an incremental improvement over existing factorization methods.
The paper tackled the problem of diffusion-like temporal delays and stretching in dynamic neuroimaging data, which limit conventional methods, by developing a shift- and stretch-invariant non-negative matrix factorization framework, demonstrating on synthetic and brain emission tomography data that it provides more detailed characterization of brain tissue structure.
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.