Fast minimum variance deconvolution

Deconvolution is an ill-posed problem and it is well known that a stochastic extension of this otherwise deterministic problem can solve this difficulty. To avoid direct inversion of huge matrices, the signal restoration may be carried out recursively by viewing the estimation problem as a degenerate case of a Kalman filter applied to a static system with time varying measurements. The major problem remaining to be solved is that of finding a practical algorithm for implementing the minimum variance estimator. A new fast algorithm of the Chandrasekhar-type is developed for a non-constant state space model and is shown to be very efficient. We also describe an application of the method to improve the range resolution of ultrasound signals.