Optimal Transport for Super Resolution Applied to Astronomy Imaging

TL;DR

This paper introduces an optimal transport-based method for super resolution in astronomy imaging, demonstrating accuracy, stability, and computational efficiency compared to neural networks.

Contribution

It presents a novel super resolution approach using optimal transport and entropy, with theoretical guarantees and practical advantages over existing neural network methods.

Findings

Achieves accurate reconstruction with known sparsity and low noise.

Proves stability and robustness of the optimizer.

Offers similar performance to neural networks with less computational cost.

Abstract

Super resolution is an essential tool in optics, especially on interstellar scales, due to physical laws restricting possible imaging resolution. We propose using optimal transport and entropy for super resolution applications. We prove that the reconstruction is accurate when sparsity is known and noise or distortion is small enough. We prove that the optimizer is stable and robust to noise and perturbations. We compare this method to a state of the art convolutional neural network and get similar results for much less computational cost and greater methodological flexibility.