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In this paper, we consider linear state-space models with compressibleinnovations and convergent transition matrices in order to modelspatiotemporally sparse transient events. We perform parameter and stateestimation using a dynamic compressed sensing framework and develop anefficient solution consisting of two nested Expectation-Maximization (EM)algorithms. Under suitable sparsity assumptions on the innovations, we proverecovery guarantees and derive confidence bounds for the state estimates. Weprovide simulation studies as well as application to spike deconvolution fromcalcium imaging data which verify our theoretical results and show significantimprovement over existing algorithms.

Efficient Estimation of Compressible State-Space Models with Application to Calcium Signal Deconvolution