FINSIG 05

FINSIG 2005Kuopio, Finland In SPECT the reconstruction is done usually off–line and all theobservation p 1 , p 2 , . . . , p T are available. The algorithm thatcomputes the estimate based on all observations, i.e. ˆθ t|T iscalled fixed interval Kalman Smoother. In addition to the KalmanFilter equations so called backward run gain matricesA t−1 = C˜θt−1F T t−1C −1˜θ t|t−1must be stored during filtering and the Smoother estimate can becomputed applying equationˆθ t−1|T = ˆθ t−1|t−1 + A t−1 (ˆθ t|T − ˆθ t|t−1 )in time–reversed (backward) order.Mikko Kervinen, Department of Applied Physics, University of Kuopio Slide 14