In this paper, we present a novel light field denoising algorithm using a vector-valued regularization operating in the 4D ray space. More precisely, the method performs a PDE-based anisotropic diffusion along directions defined by local structures in the 4D ray space. It does not require prior estimation of disparity maps. The local structures in the 4D light field are extracted using a 4D tensor structure. The paper then describes the strategy retained for setting the diffusion tensor parameters for the targeted denoising application. It then analyzes the influence of the model parameters on the denoising performance. Experimental results show that the proposed denoising algorithm performs well compared to state of the art methods while keeping tractable complexity.