Learning Geometry for Inverse Problems in Imaging

我们的社会依赖于医学、军事和广泛的工程和科学应用的数字图像数据的数量在不断增加，然而数字图像在形成、传输和存储过程中仍然表现出一定程度的退化，经常掩盖重要信息。尽管图像处理和计算机视觉领域取得了重大进展，但由于难以准确建模随机退化（如噪声、像素丢失和模糊），这个问题仍然存在。本项目的主要目标是学习关键的几何和高阶图像特征，以准确解决成像中的各种逆问题，包括图像去噪、图像去模糊、图像补漆（缺失数据的填充）和超分辨率。在这个项目中开发的新算法预计将以标准图像质量指标的形式改进现有算法，并保留准确、精细的细节，这是许多当前最先进的图像处理算法所缺少的特征，但对于在实践中自动解释这些图像数据至关重要。在最近的工作中，PI和合作者开发了几个图像去噪框架，试图从图像的去噪几何特征中恢复图像。这些方法已经成功地改进了现有的最先进的去噪算法，提供了在重建中使用替代方法难以捉摸的信息。处理这些几何数据的挑战在于，虽然它在实践中非常健壮，但为处理自然图像数据而开发的数学上合理的机制并不一定适用于它们的几何特征。该项目涉及从图像数据中学习几何描述符，这些图像数据遭受了上述随机和/或线性退化的某种组合，目的是帮助图像重建、分析和解释。初步的分析和实验表明，这种方法的好处可能是显著的，但需要计算密集的实验来探索如何在实践中最好地利用这些好处。对这些模型的理论分析也将是本项目的重要组成部分，以便更好地了解这些模型在实践中何时保证可靠。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The quantity of digital image data our society relies on for medical, military, and a wide range of engineering and scientific applications continues to increase, yet digital images still typically exhibit some level of degradation during formation, transmission, and storage, often obscuring vital information. Despite significant advances in the fields of image processing and computer vision, this problem still persists due to the difficulty in accurately modeling random degradations such as noise, pixel loss, and blur. The main objectives for this project are to learn critical geometric and higher order image features for accurately solving a variety of inverse problems in imaging, including image denoising, image deblurring, image inpainting (filling in of missing data), and super-resolution. The new algorithms developed in this project are expected to yield improvements over existing algorithms in the form of standard image quality metrics as well as in the preservation of accurate, fine details, a feature missing from many current state of the art image processing algorithms, yet vital for automatically interpreting this image data in practice. In recent work the PI and collaborators have developed several frameworks for image denoising that attempt to recover an image from a denoised geometric feature of the image. These approaches have successfully improved upon existing state of the art denoising algorithms, providing information in the reconstruction that has been elusive using alternate approaches. The challenge in working with this geometric data is that while it is very robust in practice, mathematically sound mechanisms developed for handling natural image data do not necessarily apply to their geometric features. This project involves learning geometric descriptors from image data that have suffered from some combination of the aforementioned random and/or linear degradations for the purpose of aiding in image reconstruction, analysis, and interpretation. Preliminary analyses and experiments indicate that the benefits of this approach could be significant, yet computationally intensive experiments are required to explore how best to exploit these benefits in practice. Theoretical analyses of these models will be an important part of this project as well, in order to better to understand when these models are guaranteed to be reliable in practice.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.