Blind image decomposition aims to decompose all components present in an image, typically used to restore a multi-degraded input image. While fully recovering the clean image is appealing, in some scenarios, users might want to retain certain degradations, such as watermarks, for copyright protection. To address this need, we add controllability to the blind image decomposition process, allowing users to enter which types of degradation to remove or retain. We design an architecture named controllable blind image decomposition network. Inserted in the middle of U-Net structure, our method first decomposes the input feature maps and then recombines them according to user instructions. Advantageously, this functionality is implemented at minimal computational cost: decomposition and recombination are all parameter-free. Experimentally, our system excels in blind image decomposition tasks and can outputs partially or fully restored images that well reflect user intentions. Furthermore, we evaluate and configure different options for the network structure and loss functions. This, combined with the proposed decomposition-and-recombination method, yields an efficient and competitive system for blind image decomposition, compared with current state-of-the-art methods. View paper on