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Deep neural network based methods are the state of the art in various imagerestoration problems. Standard supervised learning frameworks require a set ofnoisy measurement and clean image pairs for which a distance between the outputof the restoration model and the ground truth, clean images is minimized. Theground truth images, however, are often unavailable or very expensive toacquire in real-world applications. We circumvent this problem by proposing aclass of structured denoisers that can be decomposed as the sum of a nonlinearimage-dependent mapping, a linear noise-dependent term and a small residualterm. We show that these denoisers can be trained with only noisy images underthe condition that the noise has zero mean and known variance. The exactdistribution of the noise, however, is not assumed to be known. We show thesuperiority of our approach for image denoising, and demonstrate its extensionto solving other restoration problems such as blind deblurring where the groundtruth is not available. Our method outperforms some recent unsupervised andself-supervised deep denoising models that do not require clean images fortheir training. For blind deblurring problems, the method, using only one noisyand blurry observation per image, reaches a quality not far away from its fullysupervised counterparts on a benchmark dataset.

Unsupervised Image Restoration Using Partially Linear Denoisers