Most deep learning models for computational imaging regress a single reconstructed image. In practice, however, ill-posedness, nonlinearity, model mismatch, and noise often conspire to make such point estimates misleading or insufficient. The Bayesian approach models images and (noisy) measurements as jointly distributed random vectors and aims to approximate the posterior distribution of unknowns. Recent variational inference methods based on conditional normalizing flows are a promising alternative to traditional MCMC methods, but they come with drawbacks: excessive memory and compute demands for moderate to high resolution images and underwhelming performance on hard nonlinear problems. In this work, we propose C-Trumpets -- conditional injective flows specifically designed for imaging problems, which greatly diminish these challenges. Injectivity reduces memory footprint and training time while low-dimensional latent space together with architectural innovations like fixed-volume-change layers and skip-connection revnet layers, C-Trumpets outperform regular conditional flow models on a variety of imaging and image restoration tasks, including limited-view CT and nonlinear inverse scattering, with a lower compute and memory budget. C-Trumpets enable fast approximation of point estimates like MMSE or MAP as well as physically-meaningful uncertainty quantification.

翻译：大多数用于计算成像的深度学习模型只能回归单个重建图像。然而在实际应用中，病态性、非线性、模型失配和噪声常常导致此类点估计具有误导性或不足。贝叶斯方法将图像和（含噪声的）测量值建模为联合分布的随机向量，旨在逼近未知量的后验分布。近年来基于条件归一化流的变分推理方法作为传统MCMC方法的有前景替代方案，但仍存在缺陷：对于中高分辨率图像需要过高的内存和计算资源，且在困难非线性问题上表现欠佳。本文提出C-Trumpets——专为成像问题设计的条件性单射流，显著缓解了这些挑战。单射性降低了内存占用和训练时间，通过低维潜空间结合固定体积变化层与跳接RevNet层等架构创新，C-Trumpets在包括有限视角CT和非线性逆散射在内的多种成像及图像复原任务中，以更低的计算和内存预算优于常规条件流模型。C-Trumpets能够快速逼近MMSE或MAP等点估计，同时实现具有物理意义的不确定性量化。