Fig. 1
Workflow for dynamic mode decomposition of bleaching kinetics in fluorescence microscopy. A video sequence with decaying intensity I(x, y, t) in m frames representing time points t = 1, … m (A) gets first reshaped into a space–time matrix in which each video frame having x pixels in each row uy (here y = 3) gets reshaped into m columns with y times x elements each of a space–time matrix X (B and see Eq. 1). Following the procedure described in Eq. 2–11 the system matrix describing the fluorescence dynamics gets dimensionally reduced using a SVD and rank truncation to capture the dominant dynamics in the system. Subsequently, spectral decomposition of this truncated system matrix provides the dynamic modes (eigenfunctions), mode amplitudes and eigenvalues, which together approximate the original space–time matrix X (C). Reconstruction of the video sequence is achieved by reversing the reshaping procedure described in panel A. In this example, a rank-3 approximation of the system matrix is illustrated. See text for further explanations