While recent progress in holographic displays has shown that they are capable of displaying photorealistic 3D holograms in real time, the acquisition of high-quality real-world holograms has remained a missing piece regarding the realization of holographic streaming systems. Incoherent holographic cameras, which record holograms under daylight conditions, are suitable candidates for real-world acquisition, as they avoid the safety issue involved in the use of laser lights; however, they are hindered by severe noise due to the optical imperfections of such systems. In this work, we develop a deep learning-based incoherent holographic camera system that can deliver visually enhanced holograms in real time. A neural network filters the noise in the captured holograms, maintaining a complex-valued hologram format throughout the whole process. Enabled by the computational efficiency of the proposed filtering strategy, we demonstrate the first holographic streaming system integrating a holographic camera and a holographic display, with the aim of developing the ultimate holographic ecosystem of the future.