  We present a filtered backprojection algorithm for reconstructing the Wigner
function of a system of large angular momentum j from Stern-Gerlach-type
measurements. Our method is advantageous over the full determination of the
density matrix in that it is insensitive to experimental fluctuations in j, and
allows for a natural elimination of high-frequency noise in the Wigner function
by taking into account the experimental uncertainties in the determination of
j, its projection m, and the quantization axis orientation. No data binning and
no arbitrary smoothing parameters are necessary in this reconstruction. Using
recently published data [Riedel et al., Nature 464:1170 (2010)] we reconstruct
the Wigner function of a spin-squeezed state of a Bose-Einstein condensate of
about 1250 atoms, demonstrating that measurements along quantization axes lying
in a single plane are sufficient for performing this tomographic
reconstruction. Our method does not guarantee positivity of the reconstructed
density matrix in the presence of experimental noise, which is a general
limitation of backprojection algorithms.
