Shift- and stretch-invariant non-negative matrix factorization with an application to brain tissue delineation in emission tomography data

TL;DR

This paper introduces a shift- and stretch-invariant non-negative matrix factorization method that improves analysis of neuroimaging data by accounting for temporal delays and stretching effects, implemented in PyTorch.

Contribution

The novel framework estimates both shifts and stretches in neuroimaging data within the frequency domain, enhancing tissue characterization over traditional methods.

Findings

Successfully accounts for stretching in synthetic and real brain data.

Provides more detailed brain tissue characterization.

Implemented in PyTorch for practical use.

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.