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

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.

References in corpus (2)

• Sparsity and Incoherence in Compressive Sampling
• Generalized SURE for Exponential Families: Applications to Regularization

Cited by in corpus (6)

• Data and Physics driven Deep Learning Models for Fast MRI Reconstruction: Fundamentals and Methodologies
• Robust multi-coil MRI reconstruction via self-supervised denoising
• Enhancing quality and speed in database-free neural network reconstructions of undersampled MRI with SCAMPI
• MRI Recovery with Self-Calibrated Denoisers without Fully-Sampled Data
• Model Adaptation for Image Reconstruction using Generalized Stein's Unbiased Risk Estimator
• Deep Image Prior using Stein's Unbiased Risk Estimator: SURE-DIP