Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data

Published on May 2, 2023


We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based (diffusion) generative models trained on the underlying fully-sampled data distribution has recently been shown to outperform end-to-end supervised deep learning. In practice, such a large collection of training data may be prohibitively expensive to acquire in the first place. In this work, we present an approach for approximately learning a score-based generative model of the clean distribution, from noisy training data. We formulate and justify a novel loss function that leverages Stein's unbiased risk estimate to jointly denoise the data and learn the score function via denoising score matching, while using only the noisy samples. We demonstrate the generality of SURE-Score by learning priors and applying posterior sampling to ill-posed inverse problems in two practical applications from different domains: compressive wireless multiple-input multiple-output channel estimation and accelerated 2D multi-coil magnetic resonance imaging reconstruction, where we demonstrate competitive reconstruction performance when learning at signal-to-noise ratio values of 0 and 10 dB, respectively.


Sign up or log in to comment

Models citing this paper 0

No model linking this paper

Cite in a model to link it from this page.

Datasets citing this paper 0

No dataset linking this paper

Cite in a dataset to link it from this page.

Spaces citing this paper 0

No Space linking this paper

Cite in a Space to link it from this page.

Collections including this paper 0

No Collection including this paper

Add this paper to a collection to link it from this page.