When images are statistically described by a generative model we can use this information to develop optimum techniques for various image restoration problems as inpainting, super-resolution, image coloring, generative model inversion, etc. With the help of the generative model it is possible to formulate, in a natural way, these restoration problems as Statistical estimation problems. Our approach, by combining maximum a-posteriori probability with maximum likelihood estimation, is capable of restoring images that are distorted by transformations even when the latter contain unknown parameters. The resulting optimization is completely defined with no parameters requiring tuning. This must be compared with the current state of the art which requires exact knowledge of the transformations and contains regularizer terms with weights that must be properly defined. Finally, we must mention that we extend our method to accommodate mixtures of multiple images where each image is described by its own generative model and we are able of successfully separating each participating image from a single mixture.
Many seemingly unrelated computer vision tasks can be viewed as a special case of image decomposition into separate layers. For example, image segmentation (separation into foreground and background layers); transparent layer separation (into reflection and transmission layers); Image dehazing (separation into a clear image and a haze map), and more. In this paper we propose a unified framework for unsupervised layer decomposition of a single image, based on coupled "Deep-image-Prior" (DIP) networks. It was shown [Ulyanov et al] that the structure of a single DIP generator network is sufficient to capture the low-level statistics of a single image. We show that coupling multiple such DIPs provides a powerful tool for decomposing images into their basic components, for a wide variety of applications. This capability stems from the fact that the internal statistics of a mixture of layers is more complex than the statistics of each of its individual components. We show the power of this approach for Image-Dehazing, Fg/Bg Segmentation, Watermark-Removal, Transparency Separation in images and video, and more. These capabilities are achieved in a totally unsupervised way, with no training examples other than the input image/video itself.