Efficient Estimation of Compressible State-Space Models with Application to Calcium Signal Deconvolution
This work addresses spike deconvolution in calcium imaging, providing a more accurate method for neuroscientists, though it is incremental as it builds on existing compressed sensing and EM frameworks.
The paper tackles the problem of estimating compressible state-space models for sparse transient events, developing an efficient EM-based solution with proven recovery guarantees and confidence bounds, and demonstrates significant improvement over existing algorithms in calcium imaging spike deconvolution.
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.