Unsupervised noisy image segmentation using deep image prior

The so called Deep Image Prior paradigm stands as an exceptional advancement at the intersection of inverse problems and deep learning. By leveraging the inherent regularization properties of deep networks, Deep Image Prior has recently emerged as a landmark approach in addressing various imaging problems, including denoising, JPEG artifacts removal, inpainting, and super-resolution. The aim of this paper is to extend the Deep Image Prior idea to the segmentation of noisy images in order to benefit of both traditional variational models and new deep learning techniques. Indeed the resulting method consists of an unsupervised deep learning approach based on the minimization of very well known variational energies (such as the Mumford–Shah functional and its approximation proposed by Ambrosio and Tortorelli) properly parametrized in terms of the weights of convolutional neural networks. The implicit regularization provided by the network allows to make the traditional variational models more robust with respect to both the noise corrupting the data and the selection of the parameters which balance the role of the regularization terms. Several numerical experiments on noisy segmentation problems show promising results of the suggested approach.