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Deep learning has been widely used for solving image reconstruction tasks butits deployability has been held back due to the shortage of high-qualitytraining data. Unsupervised learning methods, such as the deep image prior(DIP), naturally fill this gap, but bring a host of new issues: thesusceptibility to overfitting due to a lack of robust early stopping strategiesand unstable convergence. We present a novel approach to tackle these issues byrestricting DIP optimisation to a sparse linear subspace of its parameters,employing a synergy of dimensionality reduction techniques and second orderoptimisation methods. The low-dimensionality of the subspace reduces DIP'stendency to fit noise and allows the use of stable second order optimisationmethods, e.g., natural gradient descent or L-BFGS. Experiments across bothimage restoration and tomographic tasks of different geometry and ill-posednessshow that second order optimisation within a low-dimensional subspace isfavourable in terms of optimisation stability to reconstruction fidelitytrade-off.

Image Reconstruction via Deep Image Prior Subspaces