Central blood pressure is a vital signal that provides relevant physiological information about cardiovascular diseases risk factors. The standard clinical protocols for measuring these signals are challenging due to their invasive nature. This makes the estimation-based methods more convenient, however, they are usually not accurate as they fail to capture some important features of the central pressure waveforms. In this paper, we propose a novel data-driven approach that combines machine learning tools and cross-relation-based blind estimation methods to reconstruct the aortic blood pressure waves from the distorted peripheral pressure signals. Due to the lack of large real datasets, in this study, we utilize virtual pulse waves in-silico databases to train the machine learning models. The performance of the proposed approach is compared with the pure machine learning-based model and the cross-relation-based blind estimation approach. In both cases, the hybrid approach shows promising results as the root-mean-squared error has been reduced by 25% with regards to the pure machine learning method and by 40% compared to the cross-relation approach.