  Signal estimation from incomplete observations improves as more signal
structure can be exploited in the inference process. Classic algorithms (e.g.,
Kalman filtering) have exploited strong dynamic structure for time-varying
signals while modern work has often focused on exploiting low-dimensional
signal structure (e.g., sparsity in a basis) for static signals. Few algorithms
attempt to merge both static and dynamic structure to improve estimation for
time-varying sparse signals (e.g., video). In this work we present a
re-weighted l_1 dynamic filtering scheme for causal signal estimation that
utilizes both sparsity assumptions and dynamic structure. Our algorithm
leverages work on hierarchical Laplacian scale mixture models to create a
dynamic probabilistic model. The resulting algorithm incorporates both dynamic
and sparsity priors in the estimation procedure in a robust and efficient
algorithm. We demonstrate the results in simulation using both synthetic and
natural data.
