In the last decade, the technological progress of multi-slice CT imaging has turned CCTA into a valuable tool for coronary assessment in many low to medium risk patients. Nevertheless, CCTA protocols expose the patient to high radiation doses, imposed by image quality and multiple cardiac phase acquisition requirements. Widespread use of CCTA calls for significant reduction of radiation exposure while maintaining high image quality as required for coronary assessment. Denoising algorithms have been recently applied to low-dose CT scans after image reconstruction. In this work, a fast neural regression framework is proposed for the denoising of low-dose CCTA. For this purpose, regression networks are trained to synthesize high-SNR patches directly from low-SNR input patches. In contrast to published methods, the denoising network is trained on real noise directly learned from noisy CT data rather than assuming a known parametric noise model. The denoised value for each pixel is computed as a function of the synthesized patches overlapping the pixel. The proposed algorithm is compared to state-of-the-art published algorithms for synthetic and real noise. The feature similarity index (FSIM) achieved by the proposed method is superior in all the comparisons with other methods, for synthetic radiation dose reductions higher than 90%. The results are further supported qualitatively, by observing a significant improvement in subsequent coronary reconstruction performed by commercial software on denoised images. The fast and high quality denoising capability suggests the proposed algorithm as a promising method for low-dose CCTA denoising.