We present a version of the Fourier-Bessel method first introduced by Fisher and coworkers and Zaroubi and coworkers with two extensions: (1) we amend the formalism to allow a generic galaxy weight that can be constant, rather than the more conventional overweighting of galaxies at high distances, and (2) we correct for the masked zones by extrapolation of Fourier-Bessel modes rather than by cloning from the galaxy distribution in neighboring regions. We test the procedure extensively on N-body simulations and find that it gives generally unbiased results but that the reconstructed velocities tend to be overpredicted in high-density regions. Applying the formalism to the PSCz redshift catalog, we find that β = 0.7 ± 0.5 from a comparison of the reconstructed Local Group velocity to the cosmic microwave background dipole. From an anisotropy test of the velocity field, we find that β = 1 cold dark matter models normalized to the current cluster abundance can be excluded with 90% confidence. The density and velocity fields reconstructed agree with the fields found by Branchini and coworkers on most points. We find a back infall into the Great Attractor region (Hydra-Centaurus region), but tests suggest that this may be an artifact. We identify all the major clusters in our density field and confirm the existence of some previously identified possible ones.
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