Underexposed images often suffer from serious quality degradation such as poor visibility and latent noise in the dark. Most previous methods for underexposed images restoration ignore the noise and amplify it during stretching contrast. We predict the noise explicitly to achieve the goal of denoising while restoring the underexposed image. Specifically, a novel three-branch convolution neural network, namely RRDNet (short for Robust Retinex Decomposition Network), is proposed to decompose the input image into three components, illumination, reflectance and noise. As an image-specific network, RRDNet doesn't need any prior image examples or prior training. Instead, the weights of RRDNet will be updated by a zero-shot scheme of iteratively minimizing a specially designed loss function. Such a loss function is devised to evaluate the current decomposition of the test image and guide noise estimation. Experiments demonstrate that RRDNet can achieve robust correction with overall naturalness and pleasing visual quality. To make the results reproducible, the source code has been made publicly available at https://aaaaangel.github.io/RRDNet-Homepage.