Imaging photoplethysmography (iPPG) is an optical technique dedicated to the assessment of several vital functions using a simple camera. Significant efforts have been made to reliably estimate heart and respiratory rates. Currently, research is focusing on the remote estimation of oxygen saturation and blood pressure (BP). The limited number of publicly available data tends to restrict the advancements related to BP estimation. To overcome this limit, we propose to split the problem in a two-stage processing chain: (i) converting iPPG to contact PPG (cPPG) signals using available video dataset and (ii) estimate BP from converted cPPG signals by exploiting large existing databases (e.g. MIMIC). This article presents the first developments where a method for converting iPPG signals measured using a camera into cPPG signals measured by contact sensors is proposed. Real and imaginary parts of the continuous wavelet transform (CWT) of cPPG and iPPG signals are passed to various deep pre-trained U-shaped architectures. Conventional metrics and specific waveform estimators have been implemented to validate the relevance of the predictions. The results exhibit good agreements towards a large portion of metrics, showing that the neural architectures properly estimated cPPG from iPPG signals through their CWT representations. The performance indicates that BP estimation from iPPG signals converted to cPPG signals can now be envisaged. Consequently, future work will focus on the integration of models dedicated to BP estimation trained on MIMIC. This is the first demonstration of a method for accurate reconstruction of cPPG from iPPG signals satisfying pulse waveform criteria.