One-pass minimum-variance deconvolution algorithms

The authors propose novel one-pass minimum-variance deconvolution (MVD) algorithms which give the MV estimate, or the approximate MV estimate, of a system's input sequence by means of just one reversed-time filter. They develop the one-pass MVD algorithm in two steps. First, by projecting the input sequence into the space spanned by the future states, they obtain a reversed-time Markov model. Then, by running a Kalman filter for this model, they obtain the MV estimate of the input sequence. In order to avoid the high computational load of the optimal algorithm, a one-pass approximate MVD algorithm which gives almost the same results as the optimal algorithm is developed. Storage requirements and operation counts of J.M. Mendel's (1983) two-pass MVD algorithm and the proposed one-pass approximate MVD algorithm are analyzed for the case of a single-channel system in controllable canonical form. The results are of interest in connection with the seismic deconvolution problem