Context. Ground-based imaging and imaging spectropolarimetric data are often subjected to post-facto reconstruction techniques to improve the spatial resolution. Aims: We test the effects of reconstruction techniques on two-dimensional data to determine the best approach to improve our data. Methods: We obtained an 1-h time-series of spectropolarimetric data in the Fe i line at 630.25 nm with the Göttingen Fabry-Pérot Interferometer (FPI) that are accompanied by imaging data in the blue continuum at 431.3 nm and Ca ii H at 396.85 nm. We apply both speckle and (multi-object) multi-frame blind deconvolution ((MO)MFBD) techniques. We use the "Göttingen" speckle and speckle deconvolution codes and the MOMFBD code in the implementation of Van Noort et al. (2005). We compare the resulting spatial resolution and investigate the impact of the image reconstruction on spectral characteristics of the Göttingen FPI data. Results: The speckle reconstruction and MFBD perform similar for our imaging data with nearly identical intensity contrasts. MFBD provides a better and more homogeneous spatial resolution at the shortest wavelength when applied to a series of image bursts. The MOMFBD and speckle deconvolution of the intensity spectra lead to similar results, but our choice of settings for the MOMFBD yields an intensity contrast smaller by about 2% at a comparable spatial resolution. None of the reconstruction techniques introduces significant artifacts in the intensity spectra. The speckle deconvolution (MOMFBD) has a rms noise in Stokes V/I of 0.32% (0.20%). The deconvolved spectra thus require a high significance threshold of about 1.0% to separate noise peaks from true signal. A comparison to spectra with a significantly higher signal-to-noise (S/N) ratio and to spectra from a magneto-hydrodynamical simulation reveals that the Göttingen FPI can only detect about 30% of the polarization signal present in quiet Sun areas. The distribution of NCP values for the speckle-deconvolved data matches that of observations with higher S/N better than MOMFBD, but shows seemingly artificially sharp boundaries and unexpected changes of the sign. Conclusions: For our imaging data, both MFBD and speckle reconstruction are equivalent, with a slightly better and more stable performance of MFBD. For the spectropolarimetric data, the higher intensity contrast of the speckle deconvolution is balanced by the smaller amplification of the noise level in the MOMFBD at a comparable spatial resolution. The noise level prevents the detection of weak and diffuse magnetic fields. Future efforts should be directed to improve the S/N of the Göttingen FPI spectra for spectropolarimetric observations to lower the final significance thresholds.