Fast one-step sampling improves image restoration and MRI reconstructions
SNaP: One-Step Posterior Sampling for Noisy Inverse Problems
Computer Vision and Pattern Recognition
Summary
Some computer programs try to fix noisy or blurry images by guessing many times, which can be very slow. The authors created a new method called SNaP that guesses just once for each fixed image, making the process much faster. Their method uses smart math to focus on the parts of the image information that are clear while allowing variations where the data is uncertain. This helps produce multiple good, different guesses very quickly for tasks like cleaning images and improving MRI scans.
What this means in practice
- •For medical imaging teams: Generate diverse high-quality MRI reconstructions with only one neural network evaluation per scan, speeding up processing greatly.
- •For image processing engineers: Create fast one-step algorithms to restore natural images affected by noise or degradation while maintaining uncertainty where data is weak.
Authors
Shirin Shoushtari, Edward P. Chandler, Xiao Shi, Ulugbek S. Kamilov
Abstract
Diffusion and flow-matching models can produce high-quality posterior samples for inverse problems, but typically require tens to thousands of network evaluations per draw. MeanFlow enables one-step generation, yet applying it to inverse problems leaves no intermediate steps at which to enforce measurement consistency. We introduce SNaP, a one-step MeanFlow posterior sampler for linear inverse problems with Gaussian noise. Its central innovation is a measurement-adapted source: a Gaussian distribution whose mean and anisotropic covariance are determined by the measurement operator, observation, and noise level. The source anchors well-measured directions while preserving variation where the measurements are weak or uninformative. We show that the exact conditional flow transports this source to the true posterior. Across natural-image restoration and multi-coil MRI, SNaP produces diverse, high-quality samples with one network evaluation per draw, 30 to 2250 $\times$ faster than iterative samplers.