High-order state space models in dynamic linear inverse problems

For dynamic linear inverse problems, where the quantity to be imaged is time-varying, joint spatio-temporal regularization methods are useful to improve reconstructions. State space models, with first-order Markov temporal dynamics, have been used to directly model the temporal evolution, and can be efficiently solved by the Kalman filter and fixed-interval smoother. Here we discuss higher-order state space models in this framework, present a decomposition structure of the decomposition, and show how, if the temporal model is a corresponding regularization matrix, and describe a Kronecker product based efficient algorithm in the case in the case of a scalar AR model.