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

• URL: http://arxiv.org/abs/2604.08161v1
• Date: Thu, 09 Apr 2026 12:22:04 GMT
• Title: Shift- and stretch-invariant non-negative matrix factorization with an application to brain tissue delineation in emission tomography data
• Abstract summary: We present the shift- and stretch-invariant non-negative matrix factorization framework.<n>Our approach estimates both integer and non-integer temporal shifts as well as temporal stretching.<n>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.
• Score: 5.529329772842872
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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