Square-root filtering in time-sequential estimation of random fields

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Abstract
As a time-sequential and Bayesian front-end for image sequence processing, we consider the square root information (SRI) realization of Kalman filter. The computational complexity of the filter due to the dimension of the problem -- the size of the state vector is on the order of the number of pixels in the image frame -- is decreased drastically using a reduced-order approximation exploiting the natural spatial locality in the random field specifications. The actual computation for the reduced-order SRI filter is performed by an iterative and distributed algorithm for the unitary transformation steps, providing a potentially faster alternative to the common QR factorization-based methods. For the space-time estimation problems, near- optimal solutions can be obtained in a small number of iterations (e.g., less than 10), and each iteration can be performed in a finely parallel manner over the image frame, an attractive feature for a dedicated hardware implementation.

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