  In this paper, we consider linear state-space models with compressible
innovations and convergent transition matrices in order to model
spatiotemporally sparse transient events. We perform parameter and state
estimation using a dynamic compressed sensing framework and develop an
efficient solution consisting of two nested Expectation-Maximization (EM)
algorithms. Under suitable sparsity assumptions on the innovations, we prove
recovery guarantees and derive confidence bounds for the state estimates. We
provide simulation studies as well as application to spike deconvolution from
calcium imaging data which verify our theoretical results and show significant
improvement over existing algorithms.
