Score-based diffusion models are frequently employed as structural priors in inverse problems. However, their iterative denoising process, initiated from Gaussian noise, often results in slow inference speeds. The Image-to-Image Schr\"odinger Bridge (I2SB), which begins with the corrupted image, presents a promising alternative as a prior for addressing inverse problems. In this work, we introduce the Measurement Embedded Schr\"odinger Bridge (MESB). MESB establishes Schr\"odinger Bridges between the distribution of corrupted images and the distribution of clean images given observed measurements. Based on optimal transport theory, we derive the forward and backward processes of MESB. Through validation on diverse inverse problems, our proposed approach exhibits superior performance compared to existing Schr\"odinger Bridge-based inverse problems solvers in both visual quality and quantitative metrics.
@article{arxiv.2407.04162,
title = {Measurement Embedded Schr\"odinger Bridge for Inverse Problems},
author = {Yuang Wang and Pengfei Jin and Siyeop Yoon and Matthew Tivnan and Quanzheng Li and Li Zhang and Dufan Wu},
journal= {arXiv preprint arXiv:2407.04162},
year = {2024}
}