2026/07/06 by Renjie He
#physics.med-ph
We build a motion suppression pipeline based on Koopman operator theory, which provides a way to turn nonlinear dynamics into linear ones by looking at the data through the right set of mathematical "lenses" (called observables). We test three versions of this idea: plain DMD that works directly on pixel values, an extended version (EDMD) that adds physically motivated features like squared intensities and spatial gradients to better capture how the MRI signal and tissue motion interact, and a neural network version that tries to learn the best features automatically. A key practical contribution is time-course repetition: we tile the entire temporal series multiple times before decomposition, which does not change the underlying dynamics but gives the algorithm more data to work with, fixing a dimensionality bottleneck that otherwise prevents the extra features from helping. The full pipeline works slice by slice, dividing each image into small overlapping blocks, applying the Koopman lifting and DMD to separate slow contrast enhancement from fast motion based on their characteristic frequencies, and blending the corrected blocks back together.