Latent linear dynamics in spatiotemporal medical data

Spatiotemporal imaging is common in medical imaging, with applications in e.g. cardiac diagnostics, surgical guidance and radiotherapy monitoring. In this paper, we present an unsupervised model that identifies the underlying dynamics of the system, only based on the sequential images. The model maps the input to a low-dimensional latent space wherein a linear relationship holds between a hidden state process and the observed latent process. Knowledge of the system dynamics enables denoising, imputation of missing values and extrapolation of future image frames. We use a Variational Auto-Encoder (VAE) for the dimensionality reduction and a Linear Gaussian State Space Model (LGSSM) for the latent dynamics. The model, known as a Kalman Variational Auto-Encoder, is end-to-end trainable and the weights, both in the VAE and LGSSM, are simultaneously updated by maximizing the evidence lower bound of the marginal log likelihood. Our experiment, on cardiac ultrasound time series, shows that the dynamical model provide better reconstructions than a similar model without dynamics. And also possibility to impute and extrapolate for missing samples.