  We present a simple and efficient Bayesian recursive algorithm for the
data-pattern scheme for quantum state reconstruction, which is applicable to
situations where measurement settings can be controllably varied efficiently.
The algorithm predicts the best measurements required to accurately reconstruct
the unknown signal state in terms of a fixed set of probe states. In each
iterative step, this algorithm seeks the measurement setting that minimizes the
variance of the data-pattern estimator, which essentially measures the
reconstruction accuracy, with the help of a data-pattern bank that was acquired
prior to the signal reconstruction. We show that with this algorithm, it is
possible to minimize the number of measurement settings required to obtain a
reasonably accurate state estimator by using just the optimal settings and, at
the same time, increasing the numerical efficiency of the data-pattern
reconstruction.
