Discovering Structure From Corruption for Unsupervised Image Reconstruction
Discovering Structure From Corruption for Unsupervised Image Reconstruction
复制标题
DOI：
10.1109/tci.2023.3325752
复制
发表时间：
2023-04
影响因子：
5.4
通讯作者：
Oscar Leong;Angela F. Gao;He Sun;K. Bouman
中科院分区：
文献类型：
--
作者：
Oscar Leong;Angela F. Gao;He Sun;K. Bouman
我们考虑解决不适定的成像逆问题，而无需访问图像先验或地面实况的例子。在这些反问题中，一个首要的挑战是，无限数量的图像，包括许多难以置信的图像，与观察到的测量结果一致。因此，需要图像先验来减少可能的解决方案的空间，以获得更理想的重建。然而，在许多应用中，很难或可能不可能获得示例图像以构建图像先验。因此，经常使用不准确的先验知识，这不可避免地导致有偏的解决方案。而不是解决一个逆问题，使用先验编码的空间结构的任何一个图像，我们建议解决一组逆问题，联合将事先约束的集体结构的基础图像。我们的工作的关键假设是，我们的目标是重建共享共同的，低维结构的底层图像。我们表明，这样的一组逆问题可以同时解决，而不使用空间图像之前，而是推断一个共享的图像生成器与低维的潜在空间。通过最大化证据下限（ELBO）的代理来找到生成器和潜在嵌入的参数。一旦被识别，生成器和潜在嵌入可以被组合以提供用于每个逆问题的重构图像。我们提出的框架可以处理一般的前向模型腐败，我们表明，来自只有少量的地面实况图像（$\leqslant 150$）的测量是足够的图像重建。我们展示了我们的方法在各种凸和非凸逆问题，包括去噪，相位恢复，黑洞视频重建。
We consider solving ill-posed imaging inverse problems without access to an image prior or ground-truth examples. An overarching challenge in these inverse problems is that an infinite number of images, including many that are implausible, are consistent with the observed measurements. Thus, image priors are required to reduce the space of possible solutions to more desirable reconstructions. However, in many applications it is difficult or potentially impossible to obtain example images to construct an image prior. Hence inaccurate priors are often used, which inevitably result in biased solutions. Rather than solving an inverse problem using priors that encode the spatial structure of any one image, we propose to solve a set of inverse problems jointly by incorporating prior constraints on the collective structure of the underlying images. The key assumption of our work is that the underlying images we aim to reconstruct share common, low-dimensional structure. We show that such a set of inverse problems can be solved simultaneously without the use of a spatial image prior by instead inferring a shared image generator with a low-dimensional latent space. The parameters of the generator and latent embeddings are found by maximizing a proxy for the Evidence Lower Bound (ELBO). Once identified, the generator and latent embeddings can be combined to provide reconstructed images for each inverse problem. The framework we propose can handle general forward model corruptions, and we show that measurements derived from only a small number of ground-truth images ($\leqslant 150$) are sufficient for image reconstruction. We demonstrate our approach on a variety of convex and non-convex inverse problems, including denoising, phase retrieval, and black hole video reconstruction.