Photonics plays an increasing role in telecommunication networks. Traditionally, optical components like fibers were only used to implement passive functionalities. Signal regeneration, in contrast, required optoelectronic conversion and further electronic means for noise rejection. In particular, the former step inevitably introduces noise all by itself, namely Johnson noise and detection shot noise. In order to avoid the detrimental influence of electronic noise, therefore, there is great interest in implementing signal regeneration in an all-optical way. Here we discuss and demonstrate a novel all-optical scheme that can amplify an amplitude modulation by about 60 dB relative to the carrier. This scheme surpasses electronic signal restoration as well as previously conceived optical concepts by orders of magnitude.