Image Reconstruction via Deep Image Prior Subspaces

TL;DR

This paper introduces a method that enhances deep image prior-based reconstruction by constraining optimization to a low-dimensional subspace, improving stability and reducing overfitting in unsupervised image reconstruction tasks.

Contribution

It proposes restricting DIP optimization to a sparse linear subspace combined with second order methods, addressing overfitting and convergence issues in unsupervised image reconstruction.

Findings

Improved stability in optimization process.

Enhanced reconstruction quality across various tasks.

Reduced overfitting to noise.

Abstract

Deep learning has been widely used for solving image reconstruction tasks but its deployability has been held back due to the shortage of high-quality training data. Unsupervised learning methods, such as the deep image prior (DIP), naturally fill this gap, but bring a host of new issues: the susceptibility to overfitting due to a lack of robust early stopping strategies and unstable convergence. We present a novel approach to tackle these issues by restricting DIP optimisation to a sparse linear subspace of its parameters, employing a synergy of dimensionality reduction techniques and second order optimisation methods. The low-dimensionality of the subspace reduces DIP's tendency to fit noise and allows the use of stable second order optimisation methods, e.g., natural gradient descent or L-BFGS. Experiments across both image restoration and tomographic tasks of different geometry and ill-posedness show that second order optimisation within a low-dimensional subspace is favourable in terms of optimisation stability to reconstruction fidelity trade-off.