Subspace mappings for image sequences

We consider the use of low-dimensional linear subspace models to infer one high-dimensional signal from another, for example, predicting an image sequence from a related image sequence. In the memoryless case the subspaces are found by rank-constrained division, and inference is an inexpensive sequence of projections. In the finite-memory case, the subspaces form a linear dynamical system that is identified via factorization, and inference is Kalman filtering. In both cases we give novel closed-form solutions for all parameters, with optimality properties for truncated subspaces. Our factorization is related to the subspace methods [8, 1] that revolutionized stochastic system identification methods in the last decade, but we offer tight finite-data approximations and direct estimates of the system parameters without explicit computation of the subspace. Applications are made to view-mapping and controlled synthesis of video textures. We demonstrate both analytically and empirically that our factorizations provide more accurate reconstructions of estimation data and predictions of held-out test-data.