Diffusion kurtosis imaging (DKI) is a promising extension of diffusion tensor imaging, giving new insights into the white matter microstructure and providing new biomarkers. Given the rapidly increasing number of studies, DKI has a potential to establish itself as a valuable tool in brain diagnostics. However, to become a routine procedure, DKI still needs to be improved in terms of robustness, reliability, and reproducibility. As it requires acquisitions at higher diffusion weightings, results are more affected by noise than in diffusion tensor imaging. The lack of standard procedures for post-processing, especially for noise correction, might become a significant obstacle for the use of DKI in clinical routine limiting its application. We considered two noise correction schemes accounting for the noise properties of multichannel phased-array coils, in order to improve the data quality at signal-to-noise ratio (SNR) typical for DKI. The SNR dependence of estimated DKI metrics such as mean kurtosis (MK), mean diffusivity (MD) and fractional anisotropy (FA) is investigated for these noise correction approaches in Monte Carlo simulations and in in vivo human studies. The intra-subject reproducibility is investigated in a single subject study by varying the SNR level and SNR spatial distribution. Then the impact of the noise correction on inter-subject variability is evaluated in a homogeneous sample of 25 healthy volunteers. Results show a strong impact of noise correction on the MK estimate, while the estimation of FA and MD was affected to a lesser extent. Both intra- and inter-subject SNR-related variability of the MK estimate is considerably reduced after correction for the noise bias, providing more accurate and reproducible measures. In this work, we have proposed a straightforward method that improves accuracy of DKI metrics. This should contribute to standardization of DKI applications in clinical studies making valuable inferences in group analysis and longitudinal studies.