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ENSURE: A general approach for unsupervised training of deep image reconstruction algorithms
Journal article   Open access   Peer reviewed

ENSURE: A general approach for unsupervised training of deep image reconstruction algorithms

Hemant Kumar Aggarwal, Aniket Pramanik, Maneesh John and Mathews Jacob
IEEE transactions on medical imaging, Vol.42(4), pp.1133-1144
04/2023
DOI: 10.1109/TMI.2022.3224359
PMCID: PMC10210546
PMID: 36417742
url
https://arxiv.org/pdf/2010.10631View
Open Access

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.

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