Low Shot Learning with Untrained Neural Networks for Imaging Inverse Problems
This addresses the challenge of data scarcity in imaging inverse problems for researchers and practitioners, offering a practical interpolation between no-data and high-data regimes, though it is incremental as it builds on existing untrained neural network methods.
The paper tackles the problem of solving linear inverse problems like compressed sensing and image colorization with limited data (5-25 examples), showing that pre-training a neural network with a few examples improves reconstruction results compared to untrained networks and matches fully trained models while using less than 1% of the data.
Employing deep neural networks as natural image priors to solve inverse problems either requires large amounts of data to sufficiently train expressive generative models or can succeed with no data via untrained neural networks. However, very few works have considered how to interpolate between these no- to high-data regimes. In particular, how can one use the availability of a small amount of data (even $5-25$ examples) to one's advantage in solving these inverse problems and can a system's performance increase as the amount of data increases as well? In this work, we consider solving linear inverse problems when given a small number of examples of images that are drawn from the same distribution as the image of interest. Comparing to untrained neural networks that use no data, we show how one can pre-train a neural network with a few given examples to improve reconstruction results in compressed sensing and semantic image recovery problems such as colorization. Our approach leads to improved reconstruction as the amount of available data increases and is on par with fully trained generative models, while requiring less than $1 \%$ of the data needed to train a generative model.