We present significant improvements in cosmic distance measurements from the WiggleZ Dark Energy Survey, achieved by applying the reconstruction of the baryonic acoustic feature technique. We show using both data and simulations that the reconstruction technique can often be effective despite patchiness of the survey, significant edge effects and shot-noise. We investigate three redshift bins in the redshift range 0.2<$z$<1, and in all three find improvement after reconstruction in the detection of the baryonic acoustic feature and its usage as a standard ruler. We measure model independent distance measures $D_{mathrm V}(r_{mathrm s}^mathrm{fid}/r_{mathrm s})$ of 1716 $pm$ 83 Mpc, 2221 $pm$ 101 Mpc, 2516 $pm$ 86 Mpc (68% CL) at effective redshifts z = 0.44, 0.6, 0.73, respectively, where $D_{mathrm V}$ is the volume-average-distance, and $r_{mathrm s}$ is the sound horizon at the end of the baryon drag epoch. These significantly improved 4.8, 4.5 and 3.4 percent accuracy measurements are equivalent to those expected from surveys with up to 2.5 times the volume of WiggleZ. These measurements are fully consistent with cosmologies allowed by the analyses of the Planck Collaboration and the Sloan Digital Sky Survey.We provide the $D_{mathrm V}(r_{mathrm s}^mathrm{fid}/r_{mathrm s})$ posterior probability distributions and their covariances. When combining these measurements with temperature fluctuations measurements of Planck, the polarization of WMAP9, and the 6dF Galaxy Survey baryonic acoustic feature, we do not detect deviations from a flat LCDM model. Assuming this model we constrain the current expansion rate to $H_0$ = 67.15 $pm$ 0.98 kms$^{-1}$Mpc$^{-1}$. Allowing the equation of state of dark energy to vary we obtain $w_mathrm{DE}$ = -1.080 $pm$ 0.135. When assuming a curved LCDM model we obtain a curvature value of $Omega_{mathrm K}$ = -0.0043 $pm$ 0.0047.
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