ENSURE: A General Approach for Unsupervised Training of Deep Image Reconstruction Algorithms

TL;DR

ENSURE introduces an unsupervised training framework for deep image reconstruction that does not require fully sampled ground-truth images, enabling effective learning in applications with limited data.

Contribution

It generalizes SURE and GSURE to handle multiple measurement operators, providing an unbiased loss function for training without fully sampled data.

Findings

Networks trained with ENSURE achieve reconstruction quality comparable to supervised methods.

ENSURE is applicable to various inverse problems beyond MRI.

The framework improves training flexibility in data-limited scenarios.

Abstract

Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data to train the deep networks is often unavailable in several applications, restricting the applicability of the above methods. We introduce a novel metric termed the ENsemble Stein's Unbiased Risk Estimate (ENSURE) framework, which can be used to train deep image reconstruction algorithms without fully sampled and noise-free images. The proposed framework is the generalization of the classical SURE and GSURE formulation to the setting where the images are sampled by different measurement operators, chosen randomly from a set. We evaluate the expectation of the GSURE loss functions over the sampling patterns to obtain the ENSURE loss function. We show that this loss is an unbiased estimate for the true mean-square error, which offers a better alternative to GSURE, which only offers an unbiased estimate for the projected error. Our experiments show that the networks trained with this loss function can offer reconstructions comparable to the supervised setting. While we demonstrate this framework in the context of MR image recovery, the ENSURE framework is generally applicable to arbitrary inverse problems.