Ensure: Ensemble Stein'S Unbiased Risk Estimator For Unsupervised Learning

Deep learning algorithms are emerging as powerful alternatives to compressed sensing methods, offering improved image quality and computational efficiency. Unfortunately, fully-sampled training images may not be available or are difficult to acquire in several applications, including high-resolution and dynamic imaging. Previous studies in image reconstruction have utilized Stein’s Unbiased Risk Estimator (SURE) as a mean square error (MSE) estimate for the image denoising step in an unrolled network. Unfortunately, the end-to-end training of a network using SURE remains challenging since the projected SURE loss is a poor approximation to the MSE, especially in the heavily undersampled setting. We propose an ENsemble SURE (ENSURE) approach to train a deep network only from undersampled measurements. In particular, we show that training a network using an ensemble of images, each acquired with a different sampling pattern, can closely approximate the MSE. Our preliminary experimental results show that the proposed ENSURE approach gives comparable reconstruction quality to supervised learning and a recent unsupervised learning method.