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：大多数计算成像的深度学习模型回归单个重建图像。然而，在实践中，病态、非线性、模型不匹配和噪声往往会共同使这些点估计具有误导性或不足。贝叶斯方法将图像和(嘈杂的)测量建模为联合分布的随机向量，并旨在近似未知变量的后验分布。基于条件归一化流的最近变分推理方法是传统 MCMC 方法的有希望的替代品，但它们具有缺点：对于中等到高分辨率的图像，需要过多的内存和计算负担，并且在难解的非线性问题上表现不佳。在这项工作中，我们提出了 C-Trumpets——专为成像问题设计的条件可逆流，大大减少了这些挑战。可逆性减少了内存占用和训练时间，低维潜空间以及架构创新，如固定体积变化层和跳跃连接 RevNet 层，使 C-Trumpets 在多种成像和图像恢复任务中优于常规的条件流模型，包括有限视 CT 和非线性逆散射，具有更低的计算和内存预算。C-Trumpets 实现了快速近似点估计，如 MMSE 或 MAP，以及物理上有意义的不确定性量化。