Abstract:

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 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 synthesis of video textures.