Robust Deep Image Recovery from Sparsely Corrupted and Sub-Sampled Measurements

Lately, two frameworks, namely deep image prior (DIP) and compressed sensing generative models (CSGM), have demonstrated remarkable performance in inverse problem solving. They accomplish this by fitting over-parameterized deep neural networks to undersampled measurements, where the network can be either trained or untrained. However, their effectiveness diminishes considerably in the presence of noise, as the over-parameterized deep neural network can easily overfit the measurements given sufficient training iterations. This study proposes a double-overparameterization approach to achieve robust image recovery when the measurements are corrupted by sparse noise. More specifically, we separate the sparse measurement noise from the clean measurement by introducing an extra sparse over-parameterization term into the training objective of DIP or CSGM. Our proposed double over-parameterization algorithm successfully mitigates the adverse effects of sparse corruptions, as demonstrated through experiments on various inverse problems with sparse corruptions.